How do you solve a serving-label question without losing the unit?
A label says a fictional snack contains 12 grams of sugar per 100 grams of product. A serving weighs 40 grams. The sugar in that serving is not 12 grams; it is 12 × 40 ÷ 100 = 4.8 grams. This small calculation contains most of the difficulty in more complicated examination problems. A number has meaning only together with its reference quantity. Change the portion, and the numerator must change with it.
G3 SEC Mathematics may place arithmetic, algebra, percentages and constraints inside an unfamiliar real-world scenario. The story could involve packaging, ingredient quantities, energy labels or any other data table. To perform well, students must translate every entry into a consistent unit, distinguish a single portion from a whole packet, state the unknowns, solve the relations and check the proposed answer against all restrictions. Accurate computation is only the middle of the method. Interpretation and checking decide whether the answer fits the question.
Quick route: read the column headings; identify the reference mass; convert all amounts to a common base; state the number and size of portions; construct equations for unknown quantities; check whole-number restrictions, money and stock; calculate percentages with the correct denominator; round at the required stage; and write a conclusion that addresses the question. These examples use fictional labels to practise Mathematics, not to prescribe a diet or evaluate anyone’s nutrition.
What the official 2027 G3 Mathematics assessment requires
The Singapore–Cambridge Secondary Education Certificate starts in 2027. The G3 Mathematics code is K310, succeeding the former O-Level Mathematics code 4052. According to the 2027 SEC G3 catalogue and K310 syllabus, Mathematics has two papers, each lasting 2 hours 15 minutes and each contributing 50% of the total assessment. Paper 1 has approximately 26 short-answer questions. Paper 2 comprises 9 to 10 longer questions and includes a real-world scenario in its final question. Calculators are permitted in both. Working should be shown where it supports the solution. Unless the question states otherwise, non-exact numerical answers are generally given to three significant figures, with angles in degrees to one decimal place. Follow the actual paper’s instructions rather than assuming every situation must be rounded identically. The serving-label scenarios here are original mathematics practice, not a forecast of actual examination topics.
Own the mathematical intent, not somebody else’s subject
Volume 0555 explains digestion, absorption and villi in Biology. It does not establish what an individual should eat or how a particular meal affects health. This volume has a different owner: ratio, proportion, unit conversion, simultaneous equations, percentage calculations and feasibility decisions in a small fictional inventory model. It also builds on Volume 0552, which protects meaning when the number is a sampling time rather than an exact endpoint, and Volume 0554, which teaches a cross-subject evidence audit. The G3 Mathematics tutorial route owns the broader algebra revision. Use the complete G3 SEC guide for the connected examination sequence. The contextual vocabulary is deliberately simple so that the mathematical obstacle stays visible.
First establish the reference quantity
A label headed “per 100 g” means that the listed amounts correspond to 100 grams of the food. A label headed “per serving” refers to the particular serving size printed with it, not necessarily 100 grams. A label headed “per pack” refers to the entire pack, which may contain multiple servings. Before doing any arithmetic, rewrite the heading in words. For example, “8 g of protein per 100 g of product” means 8 grams of protein for every 100 grams of product represented by the label’s figures. The rate has a denominator. Writing only “8 g” loses the relationship needed to scale the value. This is the same discipline taught by the PSLE guide on keeping the word per attached to its divisor. At G3, that habit extends to algebraic models and constraints.
The scaling rule is one proportional relationship
If a product contains a grams of a substance for every 100 grams of product, then a serving of m grams contains a × m ÷ 100 grams, assuming the composition is uniform. For example, 12 g per 100 g gives 12 × 40 ÷ 100 = 4.8 g in a 40 g serving. The intermediate value 12 ÷ 100 = 0.12 represents grams of substance per gram of product. Multiplying by 40 g gives the correct substance amount. Write the units during revision. Even when an exam answer is given in a short line, checking the dimensions prevents the common mistake of multiplying by 100 instead of dividing by it.
A complete fictional two-product table
Suppose Product A has a stated protein amount of 8 g per 100 g, a sugar amount of 12 g per 100 g, and an illustrative energy value of 360 kcal per 100 g. Its listed serving is 40 g. Product B has protein 5 g per 100 g, sugar 6 g per 100 g and energy 80 kcal per 100 g; its listed serving is 150 g. For A, one serving corresponds to 3.2 g protein, 4.8 g sugar and 144 kcal. For B, one serving corresponds to 7.5 g protein, 9 g sugar and 120 kcal. These are invented numerical inputs. The calculation method is general, but the table is not a recommendation about real foods or personal nutritional needs. Write down the derived per-serving row before attempting a combination problem.
What the unit of a variable should say
In a word problem, x is not a mysterious symbol. It might represent the number of 40 g servings of Product A, the mass in grams of Product A, or the number of whole boxes purchased. These are different variables. Write “let x be the number of 40 g servings of A” before constructing an equation. If x means servings, then 3.2x represents grams of protein supplied by those A servings. If x means grams of A, the expression becomes 0.08x. Both can be correct, but they cannot be interchanged without conversion. Many mistakes appear to be algebra errors when the true problem is that the unknown was never defined.
The basic total equation
Let x be the number of A servings and y the number of B servings in the fictional table. Their total protein is 3.2x + 7.5y grams. Their total sugar is 4.8x + 9y grams. The total number of servings is x + y. If each A serving costs $1.20 and each B serving costs $1.80, the total purchase cost is 1.20x + 1.80y dollars. Each coefficient carries a different unit, so the equations must be interpreted separately. Adding protein and money in one expression is meaningless unless the scenario explicitly defines a combined scoring function with appropriate units. The common algebraic structure does not make the physical quantities equivalent.
Two simultaneous equations can identify a combination
For a cleaner integer demonstration, imagine two fictional packs rather than the previous per-serving products. Pack C contains 4 g of one measured nutrient and 6 g of another; Pack D contains 7 g of the first and 2 g of the second. A hypothetical total gives 26 g of the first nutrient and 22 g of the second. Let x and y be whole packs. Then 4x + 7y = 26 and 6x + 2y = 22. Divide the second equation by 2 to obtain 3x + y = 11, so y = 11 − 3x. Substitute into the first: 4x + 7(11 − 3x) = 26; therefore −17x = −51, x = 3 and y = 2. Check: 4(3) + 7(2) = 26 and 6(3) + 2(2) = 22. This is a mathematical reconstruction of packs from totals, not a meal suggestion.
Why you must check both original equations
Finding x = 3 and y = 2 is not the end of the reasoning. Substitute the values into the original pair rather than only the simplified expression. The first total is 12 + 14 = 26, and the second is 18 + 4 = 22. Both match. Check that the variables are non-negative whole numbers because they count whole packs. If a solution were 2.5 packs and the problem permitted only sealed complete packs, the algebraic solution might satisfy the equations but fail the practical constraint. A correct mathematical answer is one that satisfies every given condition, not only the equation you happened to solve first.
Whole packs, fractional servings and feasibility
The wording determines whether a quantity is discrete or continuous. A mass of loose ingredients may be measured in fractions of a gram, subject to stated accuracy. A count of intact sealed packets must be a non-negative integer. A question might permit cutting a bar in half while forbidding the purchase of half a sealed multipack. Read those distinctions. If a computed x is 2.4 and x counts whole packs, rounding it to 2 or 3 could violate an exact nutrient target. Instead, say that the equality constraints have no allowed whole-number solution unless another permitted combination exists. When the question asks for at least a target rather than exactly a target, different feasible integer combinations may be acceptable.
Inequalities tell a different story from equalities
“Exactly 26 g” is modelled by an equality. “At least 26 g” is modelled by an inequality such as 4x + 7y ≥ 26. “No more than $9” is modelled by 1.20x + 1.80y ≤ 9. These are not interchangeable. An equality may have one solution in two unknowns only when accompanied by enough independent information; an inequality can permit many. In an examination problem, underlining phrases such as at least, fewer than, more than, no more than and exactly helps prevent the solver from building the wrong mathematical model. Boundary words are part of the data, not decorative English.
Percentages demand a named whole
Suppose 4.8 g sugar appears in a 40 g serving. The mass percentage of sugar is 4.8 ÷ 40 × 100% = 12%, consistent with the “12 g per 100 g” entry. If a different serving contains 9 g sugar in a 150 g portion, the percentage is 9 ÷ 150 × 100% = 6%. Comparing 4.8 and 9 as absolute grams answers a different question from comparing 12% and 6% concentration. Neither comparison describes health quality. For mathematical interpretation, always state whether the reference is total serving mass, the initial amount, the final amount or some other base. The PSLE percentages guide explains why changing the whole changes the answer.
Percentage increase is directional
If a hypothetical ingredient’s price changes from $1.20 to $1.50, the increase is $0.30 and the percentage increase relative to the original price is 0.30 ÷ 1.20 × 100% = 25%. Moving from $1.50 back to $1.20 is a decrease of 0.30 ÷ 1.50 × 100% = 20%. These percentages differ because the denominators differ. Students often mistakenly claim they must be equal because the dollar difference is symmetrical. Write the baseline beside every percentage change. In a multi-step scenario, distinguish the price before a discount, the reduced price, and the price after tax rather than applying unrelated percentages to the wrong reference quantity.
Averages of ratios must respect group sizes
Suppose a trial includes ten 40 g A servings and two 150 g B servings. The combined sugar is 10 × 4.8 + 2 × 9 = 66 g. The combined product mass is 10 × 40 + 2 × 150 = 700 g. Sugar accounts for 66 ÷ 700 × 100% ≈ 9.43% by mass. It would be wrong to take the ordinary average of 12% and 6%, which is 9%, because the two product masses differ. A weighted calculation uses the total numerator and total denominator. This distinction carries beyond labels to pooled rates, prices per unit, speeds and population percentages. Always ask what quantity is being weighted.
Two ways to make an answer more transparent
A table can list mass and ingredient content for each product, then a total row. Algebra can express the same relationship. Use the form that reveals the question’s structure most directly. For one product and one portion, a single line of proportion may be fastest. For unknown numbers of packs, write simultaneous equations. For a decision under several restrictions, a compact candidate table can make feasibility checks easier. Do not copy every number from a narrative into arithmetic immediately. First choose a representation that separates the unknowns, rates and constraints. Efficiency comes from modelling the right problem before calculating.
Price per kilogram and price per serving are different comparisons
A 400 g package costing $6 has a price of $6 ÷ 0.4 kg = $15 per kilogram. If its serving is 40 g, it contains ten servings and costs $0.60 per serving, assuming each portion is equal. Another package priced at $4 for 200 g costs $20 per kilogram, but may have a different serving size. A claim that a pack is “cheaper” can refer to purchase price, price per gram or price per serving. Decide which criterion the question asks for. Do not compare $6 with $4 and conclude the first has a higher unit price without considering the masses. The unit of the answer should make the interpretation explicit.
Stock limits and budget limits are separate constraints
A fictional shop has at most four packs of C and at most five packs of D. The conditions are x ≤ 4 and y ≤ 5, with x and y non-negative integers. If C costs $2 and D $3, a $15 budget gives 2x + 3y ≤ 15. A pair such as x = 3, y = 2 satisfies the budget because 6 + 6 = 12, and it is within both stock limits. A pair x = 5, y = 1 may satisfy the budget but violates the C stock limit. It is insufficient to check only one inequality. When candidates have to select the best feasible combination, write a short justification for why the winner beats the other admissible options under the stated goal.
A whole-number search can be systematic
If two unknowns must be non-negative integers and the stock limits are small, enumerate feasible pairs rather than guessing. Let x range from zero to the maximum number of C packs. For each x, determine the possible integer values of y within the remaining budget and stock. Evaluate the target expression only for these pairs. This is a structured mathematical method, not an invitation to run an unsafe real-world experiment. In an exam, show enough of the enumeration that the marker can see you did not ignore a feasible candidate. If a closed-form algebraic solution exists, use it; if multiple inequalities define a small region, orderly enumeration can be clearer.
Rounding belongs near the end
Suppose one mathematical calculation produces 7.4996 g. If the task requests three significant figures, the reported value is 7.50 g, with the trailing zero communicating the number of significant figures. But if this value is part of a later exact comparison with a threshold of 7.50 g, premature rounding could change the decision. Keep unrounded values during the working and apply the instructed rounding to the final reported answer, except where the question specifies otherwise. An inequality involving a whole-pack count needs careful treatment: a required count of at least 3.2 whole packs means at least four, not three. Rounding rules follow the variable’s meaning as well as the printed instruction.
A units audit after solving
Before writing a final answer, check every expression using dimensions. “6 g per 100 g × 150 g” gives 9 g of the measured substance after division by 100 g. “$2 per pack × 4 packs” gives $8. “8 g of protein per serving × 3 servings” gives 24 g of protein. An answer of 24 g per serving for the last calculation would be a unit mistake even though the number 24 is arithmetically correct. Unit analysis is a cheap and reliable final control: if the units on the two sides of an equation cannot match, recheck the variable definition, rate or conversion.
A scenario can contain irrelevant labels
In a real-world Mathematics problem, a table may contain several columns, but a particular question may ask only about price and mass. Do not automatically convert energy, protein, sugar, fibre, serving number and every other entry merely because they are present. Circle the quantities needed for the question. A later part may use another column; return to the source then. The skill is selective reading, not avoidance of unfamiliar words. Technical context should not hide the mathematical operation. If a number has no role in the stated constraints or objective, leave it out and explain the chosen model if necessary.
A compact five-stage paper strategy
First identify what the question wants: a mass, total, ratio, price, percentage, number of packs or feasibility decision. Second define the variable and its unit. Third translate the appropriate rates into equations or inequalities. Fourth solve with clear working and reasonable accuracy. Fifth check the result against the original table, all constraints and the practical meaning of a whole pack or serving. A student who reaches a plausible number by intuition still needs to show enough working for a structured Mathematics item. A student who completes the algebra but never answers the final decision question has left the task unfinished.
Practise without turning Mathematics into personal nutrition advice
These serving-label cases are designed to teach proportion and data interpretation. They do not set appropriate amounts of sugar, protein or energy for any person, nor do they claim a product is healthy or unhealthy. The labels and targets are hypothetical mathematical inputs. In the classroom, keep the question on arithmetic relationships and stated constraints. The Biology digestion volume explains nutrient pathways, but neither volume should be used to draw individual health conclusions from a toy model. Students can practise the same operations using paper supplies, bottles of water or bus fares; the mathematical reasoning transfers across contexts.
Twenty-eight worked mathematics clinics
Try each numerical decision without the answer first. The explanations give working, units and a reason to accept or reject an interpretation.
Worked clinic 1: One serving from a per-100 g label
A fictional product lists 15 g fibre per 100 g and has a 30 g serving. Multiply 15 × 30 ÷ 100 = 4.5 g fibre per serving. The denominator is 100 g of product, not 100 servings. Check by noting that 30 g is less than one third of 100 g, so the answer should be less than 5 g. This quick estimate is a useful defence against a misplaced decimal.
Worked clinic 2: A packet with several servings
A 240 g packet is divided into 30 g portions. It contains 240 ÷ 30 = 8 equal servings. If one portion contains 2.4 g of a listed component, the whole packet has 8 × 2.4 = 19.2 g. The answer describes the full packet. Be explicit about the distinction; 2.4 g is a per-serving figure, while 19.2 g is a per-packet total.
Worked clinic 3: Converting 0.75 kg
A mass of 0.75 kg is 750 g because 1 kg equals 1000 g. If the product contains 7 g per 100 g of a component, the total is 7 × 750 ÷ 100 = 52.5 g. A common wrong answer treats 0.75 as grams or forgets to divide by 100. Put all masses in the same unit before applying the ratio.
Worked clinic 4: A fraction of a listed serving
One full 60 g portion contains 9 g of a substance. A half-portion is 30 g and contains 4.5 g, assuming uniform composition. It would be incorrect to keep the 9 g because the serving unit changed. Fractions of a portion may be allowed in a mass question even if fractions of sealed packs are not allowed in a purchasing question.
Worked clinic 5: Reverse the label calculation
A 50 g portion is said to contain 4 g of a component. Per 100 g, the amount is 4 ÷ 50 × 100 = 8 g. This is an inverse scaling question. A quick check: doubling the portion mass to 100 g should double the component amount from 4 g to 8 g. Do not reverse the proportional direction.
Worked clinic 6: Equal grams, different concentrations
Portion P contains 6 g in 60 g product, and portion Q contains 6 g in 120 g product. They have equal absolute amounts but different mass percentages. P is 6 ÷ 60 × 100% = 10%; Q is 6 ÷ 120 × 100% = 5%. State which comparison the question requires; absolute grams and percentage concentration are not interchangeable.
Worked clinic 7: A mixed product total
Two A servings each have 4.8 g of sugar, while one B serving has 9 g in the fictional table. Combined sugar is 2 × 4.8 + 9 = 18.6 g. The associated product mass is 2 × 40 + 150 = 230 g. If the question asks only total sugar, do not unnecessarily compute mass percentage. If it asks percentage, use 18.6 ÷ 230 × 100% ≈ 8.09%.
Worked clinic 8: The whole is not the serving count
Three boxes each contain 10 equal servings. A pupil divides a measured total by three instead of thirty when asked for the amount per serving. Three is the number of boxes; thirty is the number of servings. Write both units explicitly. A total of 90 g over thirty servings means 3 g per serving, not 30 g per serving.
Worked clinic 9: Unit price per kilogram
A 350 g pack costs $5.25. The mass is 0.35 kg and the unit price is $5.25 ÷ 0.35 = $15 per kg. A plausible shortcut is 5.25 × 1000 ÷ 350. Both methods agree. If the result appears as $0.015 per kg, the denominator conversion is almost certainly inverted.
Worked clinic 10: Unit price per serving
A 500 g pack costs $10 and contains ten equal 50 g servings. Each serving costs $10 ÷ 10 = $1. A second pack costing $8 could still be more expensive per serving if it provides fewer portions. The total purchase price alone does not settle the per-serving comparison.
Worked clinic 11: An equation in packs
Pack C contributes 4 units and pack D contributes 7 units of a hypothetical quantity. Write 4x + 7y = 26 when the total is exactly 26 units. Do not use x + y = 26 unless the quantity being counted is the number of packs. The coefficients are essential: they say how many units each pack contributes.
Worked clinic 12: Solve by elimination
Given 4x + 7y = 26 and 6x + 2y = 22, simplify the second to 3x + y = 11. Substitute y = 11 − 3x to get 4x + 77 − 21x = 26, so x = 3 and y = 2. Show this reasoning, then verify both totals. The pair is not merely a guess.
Worked clinic 13: A fractional solution violates a stock rule
An algebraic solution yields x = 2.5 for the number of sealed packs. The problem forbids partial packs. It is incorrect to state that 2.5 sealed packs are available or to round without checking whether the rounded pair still satisfies all equalities. The conclusion may be that no permitted exact solution exists; alternatively a different integer pair may satisfy an inequality version of the problem.
Worked clinic 14: At least versus exactly
A requirement of at least 18 units is expressed as a total greater than or equal to 18, not equal to 18. A combination giving 20 units may be feasible if other constraints hold. If the target had said exactly 18, a total of 20 would not satisfy it. Translate the boundary word before solving.
Worked clinic 15: Budget and stock together
C costs $2 each, D costs $3 each, and at most four C and five D are stocked. For x = 3 and y = 2 the cost is 2 × 3 + 3 × 2 = $12. The stock restrictions are also met. For x = 5 and y = 1, cost is $13 but the C stock restriction fails. A budget test by itself is incomplete.
Worked clinic 16: A percentage increase from the original
A fictional pack rises in price from $4 to $5. The increase is $1; relative to $4 this is 25%. A common error divides by the new price $5 and reports 20%. That 20% would describe a different, reverse comparison. State the original reference in words.
Worked clinic 17: A reverse decrease
A price falls from $5 to $4. The reduction is $1 ÷ $5 × 100% = 20%. It is not 25% simply because the reverse price rise is 25%. The amount changed is the same dollar, but the whole has changed. This is a good quick test of whether students understand denominators.
Worked clinic 18: The weighted mixture percentage
Ten A servings contribute 48 g sugar in 400 g product. Two B servings contribute 18 g sugar in 300 g product. The combined percentage is (48 + 18) ÷ (400 + 300) × 100% = 66 ÷ 700 × 100% ≈ 9.43%. Do not take the unweighted average of 12% and 6% without regard to the masses.
Worked clinic 19: A table with an irrelevant column
A question asks which package has the lower cost per 100 g. The table includes illustrative energy and nutrient entries as well as price and mass. Use only price and mass. For a $6 400 g pack, cost per 100 g is $1.50; for a $4 200 g pack it is $2. The first has the lower unit price despite the higher initial purchase price.
Worked clinic 20: Rounding 7.4996
If a non-exact final result must be given to three significant figures, 7.4996 rounds to 7.50. The zero is significant. If it is an intermediate result in an inequality, retain the unrounded value until the decision is made. Avoid using a rounded intermediate to force a boundary result.
Worked clinic 21: A whole number at a lower bound
At least 3.2 sealed boxes are required by a computed lower bound. Because a fraction of a sealed box cannot be bought under the given condition, the minimum permissible count is 4. Ordinary rounding to the nearest integer would give 3, which fails the requirement. This is an interpretation of an inequality, not a three-significant-figure instruction.
Worked clinic 22: A wrong unit survives correct arithmetic
A student calculates 8 g per serving × 3 servings = 24 and writes ’24 servings’. The numerical multiplication is right, but the unit is wrong. The product is 24 g of the listed component. Read the units aloud in the equation before finalising the answer.
Worked clinic 23: A ‘per pack’ line mistaken for ‘per serving’
A label says 20 g per pack and clearly lists four servings in the pack. If equal, the amount per serving is 20 ÷ 4 = 5 g. Multiplying by four would incorrectly treat the pack total as a serving total. When two headings are printed near each other, rewrite them on separate lines before calculating.
Worked clinic 24: Two solutions with the same cost
Combination P uses three C packs and two D packs: with $2 and $3 prices, the cost is $12. Combination Q uses six C packs and no D packs: also $12, but Q may violate a stock limit of four C packs. Equal cost does not mean equal feasibility. The question may impose other constraints, and the solver must compare all of them.
Worked clinic 25: A scenario with no feasible pair
A problem requires at least six D packs but states that the shop has at most five. No choice of x can repair this contradiction. Write that the conditions cannot be satisfied, and identify the conflicting inequalities y ≥ 6 and y ≤ 5. A solver who produces a large numerical answer without checking stock has failed to understand the model.
Worked clinic 26: Interpreting a ratio in words
If the ratio of C packs to D packs is 3:2, write x:y = 3:2 or x = 3k and y = 2k for a common k. For a whole-pack question k must be chosen so both counts are integers. The ratio 3:2 is not the same as ‘C is three packs more than D’. Check whether a question states a difference or a multiplicative comparison.
Worked clinic 27: An unfamiliar unit is harmless if defined
An original question defines 1 measure as 250 mg. Four measures total 1000 mg, or 1 g because 1000 mg = 1 g. Do not import an unrelated idea about nutrition or assume mg means milligrams of the entire product. Mathematical unit conversion is determined by the stated definition and ordinary metric relationships.
Worked clinic 28: A final recommendation without a reason
Two feasible packaging combinations have costs $14 and $12, with identical target fulfilment. If the instruction asks for the cheaper combination, state the $12 one and cite the difference of $2. If it asks for the highest remaining stock, a different criterion applies. An answer that simply says ‘choose B’ without calculating or connecting to the specified objective leaves the result unsupported.
Full original multi-part examination practice
A school is preparing a purely fictional stock exercise. Package C costs $2, provides four units of Component P and six of Component Q. Package D costs $3, provides seven units of P and two of Q. It has five C packs and four D packs available. Students are asked to find whole-number pack counts that give exactly 26 units of P and 22 units of Q; determine the cost; and decide whether the choice meets a $15 budget.
Let x be the number of C packs and y the number of D packs. The component equations are 4x + 7y = 26 and 6x + 2y = 22. Simplifying the second gives 3x + y = 11; substituting y = 11 − 3x into the first gives 4x + 77 − 21x = 26, hence x = 3. Then y = 2. Both original equations check. The cost is 2(3) + 3(2) = $12, within the $15 budget. The stock constraints are satisfied because 3 ≤ 5 and 2 ≤ 4. The whole-number requirement is also satisfied. Therefore the stated combination is feasible.
Part B asks whether swapping one C pack for one D pack preserves the exact targets. The changed pair is x = 2, y = 3. The P total becomes 4(2) + 7(3) = 29, not 26, and the Q total becomes 6(2) + 2(3) = 18, not 22. The cost becomes 2(2) + 3(3) = $13, but price alone cannot make it a valid alternative. The exact-content requirements fail. This example illustrates an important principle: changing one decision variable often changes several results at once. Check every required equality and inequality after any proposed substitution.
Part C changes the requirement to at least 26 units of P and at least 22 units of Q, with a total budget no greater than $15. The original pair remains feasible. Other pairs might also be feasible, so the solution is no longer automatically unique. A systematic comparison could enumerate whole-number pairs within 0 ≤ x ≤ 5, 0 ≤ y ≤ 4 and 2x + 3y ≤ 15, then check both component lower bounds. The task is now an integer feasibility problem rather than merely simultaneous linear equations. Do not assume that because the pair x = 3, y = 2 was unique for the exact equalities it must be the only pair satisfying the looser inequalities.
A seven-day arithmetic and modelling routine
Day one: convert per-100 g labels to several serving sizes. Day two: reverse the calculation from a serving figure to a unit rate. Day three: practise denominators in mass percentages and changes. Day four: solve simultaneous equations with carefully defined variables. Day five: add whole-pack, price and stock constraints. Day six: work a combined table problem, retaining full working and correct units. Day seven: mark your own solution against the original scenario and identify the first mistaken assumption. Return to the weak step instead of merely memorising the correct final number. If a future question uses tickets, paint, stationery or transport fares, the same mathematical route should still work.
Final checks and official references
Use the 2027 SEC G3 syllabus catalogue and Mathematics K310 syllabus for authoritative assessment details. The example food labels, target amounts and purchasing constraints on this page are fictional training data, not health guidance. Students should not use a constrained arithmetic exercise to decide personal dietary needs. In an examination, read the actual question, show appropriate working and obey its stated rounding instructions.
The most reliable way to solve a contextual problem is to keep quantities attached to their units and conditions. Once the model is true to the question, the algebra becomes easier. The next English volume asks students to read a non-narrative information text, explain its language choices and distinguish what a claim says from what a reader might infer. That is the language partner to the Mathematics habit developed here.
