Topics › Algebra › Q106
Algebra · simplify and substitute
P6 · Algebra · PSLE Maths
Question
At a school carnival, Siti bought n game coupons. Ali bought 2 more coupons than Siti. Raju bought 3 times as many coupons as Ali. Mei Ling bought 5 fewer coupons than Raju. If n = 17, how many coupons did the four children buy altogether? (First form and simplify an expression in n.)
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Hint
First express each child’s number of coupons in terms of n. Then add the four expressions and collect like terms.
Show the answer and step-by-step explanation
Answer: Total 145 coupons
- Draw the model — First draw a bar model for the number of coupons each child bought. Siti has n; Ali has 2 more.
- Show multiples — Raju has 3 times as many as Ali, so he has 3 groups of (n + 2). Mei Ling has 5 fewer than Raju.
- Write expressions — Now write each child’s number of coupons in terms of n. Remember: Mei Ling has Raju’s amount, then 5 less.
- Add and simplify — The total is the sum of the four expressions. Expand the brackets first, then collect the n terms and the numbers.
- Substitute n = 17 — The question gives n = 17. Substitute 17 into the simplified expression 8n + 9 to calculate faster.
- Answer and recap — So the four children bought 145 coupons altogether. Check: Siti 17, Ali 19, Raju 57, Mei Ling 52; 17 + 19 + 57 + 52 = 145. 📌 Key idea: form the expression, simplify it, then substitute the value. This makes the calculation clearer and less error-prone.
Method: Let the unknown be n and write an algebraic expression for each quantity. For the total, add the expressions, expand brackets, collect like terms, then substitute the value of n.
Practice: 3 similar questions
- Ben has x postcards. Ali has 4 more postcards than Ben. Mei Ling has twice as many postcards as Ali. If x = 9, how many postcards do they have altogether?
Answer
48 postcards — Total for the three children: x + (x + 4) + 2(x + 4). Simplify: x + x + 4 + 2x + 8 = 4x + 12. Substitute x = 9: 4 × 9 + 12 = 48.
- Raju has p bookmarks. Siti has 3 fewer bookmarks than Raju. Ali has twice as many bookmarks as Raju. Mei Ling has twice as many bookmarks as Siti. If p = 15, how many bookmarks do the four children have altogether?
Answer
81 bookmarks — Total: p + (p − 3) + 2p + 2(p − 3). Simplify: p + p − 3 + 2p + 2p − 6 = 6p − 9. Substitute p = 15: 6 × 15 − 9 = 81.
- For a class party, each box contains y muffins. Ali bought 4 boxes. Siti bought 2 boxes and 5 extra muffins. Raju bought 3 boxes but gave 7 muffins to the teacher. If y = 12, how many muffins did they have altogether in the end?
Answer
106 muffins — Total: 4y + (2y + 5) + (3y − 7). Simplify: 4y + 2y + 5 + 3y − 7 = 9y − 2. Substitute y = 12: 9 × 12 − 2 = 106.
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