The pattern
Constant total
Money moves between two people, so their total never changes.
Money, cookies or pebbles move from one person to the other, but none of it leaves the two people. So their total is the same before and after. Draw the before and the after cut into the same number of shares, and that fixed total tells you what one share is worth.
How to spot it
One person gives, sells or loses an amount to the other, and nobody outside the two people gains or loses anything.
Common mistake
Children draw different totals before and after, or forget that moving an amount from one person to the other changes the gap between them by twice that amount.
19 worked solutions
Standard
- Liam and Noah's cards — 7 : 5 becomes 5 : 7 The ratio of Liam's trading cards to Noah's trading cards was 7 : 5. After Liam gave some of his cards to Noah, the ratio became 5…
- Marbles — equal after a transfer Ali had 3 times as many marbles as Ben. After Ali gave 24 marbles to Ben, the two boys had the same number of marbles. How many ma…
- Mrs Tan and her son — money made equal Mrs Tan had 4 times as much money as her son. After she gave him $18, the two of them had the same amount of money. How much money…
- Nadia and Priya's beads — what Nadia gave In a craft class, the ratio of Nadia's beads to Priya's beads was 4 : 1. After Nadia gave some of her beads to Priya, the ratio be…
- Sara and Tom's savings — what Sara gave The ratio of Sara's savings to her brother Tom's savings was 5 : 1. After Sara gave some of her savings to Tom, the ratio became 2…
- Stickers — Mei and Priya end up equal Mei had 5 times as many stickers as Priya. After Mei gave 40 stickers to Priya, the two girls had the same number of stickers. How…
- Stickers — Mei gives some to Jun The ratio of Mei's stickers to Jun's stickers was 7 : 3. After Mei gave some stickers to Jun, the ratio became 3 : 2. Together the…
- Trading cards — Ravi gives Zack 90 Ravi had 7 times as many trading cards as Zack. After Ravi gave 90 trading cards to Zack, the two boys had the same number of trad…
Challenging
- Chocolates — all three end equal Alina, Betty and Cindy shared some chocolates. Alina had 1/11 of the total, Betty had 25% as many as Cindy, and Cindy gave 104 cho…
- Container P and Container Q held marbles in the ratio 9 : 7. After 20 marbles were poured from Container P into Container Q, the ratio became 7 : 9. How many marbles were in Container P at fi…
- Cookies — Box A and Box B swap The ratio of cookies in Box A to cookies in Box B was 5 : 3. After 16 cookies were moved from Box A to Box B, the ratio became 3 :…
- Game cards — a fifth changes hands Alex and Jamie had the same number of game cards. After Jamie lost 20% of his game cards to Alex, Jamie had 30 cards fewer than Al…
- Ken and Mei's piggy banks held money in the ratio 3 : 1. After Ken transferred $30 to Mei's piggy bank, the ratio became 1 : 3. How much money did Ken have at first?
- Marbles — Priya and Zara swap shares Priya and Zara had a total of 160 marbles. Priya gave 1/3 of her marbles to Zara. Zara then gave 1/5 of her marbles to Priya. In t…
- Marbles — Ravi, Suresh and Tara end up equal Ravi, Suresh and Tara shared some marbles. Ravi had 1/7 of the total, Suresh had 40% as many as Tara, and Tara gave 82 marbles to …
- Maya and Liam had stickers in the ratio 7 : 5. After Maya gave 18 stickers to Liam, the ratio became 5 : 7. How many stickers did Maya have at first?
- Mr. Tan and Mr. Lim had the same number of stamps in their collections. After Mr. Tan gave 15% of his stamps to Mr. Lim, Mr. Tan had 2…
- Pebbles — Ali and Ben end up equal Ali and Ben had a total of 100 pebbles. Ali gave 2/7 of his pebbles to Ben. Ben then gave 1/6 of his pebbles to Ali. In the end, e…
- Trading cards — Farah and Wei Ling Farah and Wei Ling had a total of 180 trading cards. Farah gave 1/4 of her trading cards to Wei Ling. Wei Ling then gave 1/3 of he…
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.