The pattern
Constant part
The ratio changes, but one person's amount stays the same.
A ratio is given before and after, and one person keeps what they started with while an amount is added to the other. Draw both so the person who never changed is cut into the same number of shares each time. The amount added then sits against a fixed number of shares, and one share can be worked out.
How to spot it
A ratio changes and the question tells you only one person gained or lost an amount, while the other kept what they had.
Common mistake
Children keep the same number of shares for the person whose amount did not change. The amount stays the same, but the size of a share can differ between the two ratios.
8 worked solutions
Challenging
- Ali and Ben's savings — the ratio shifts The ratio of Ali's savings to Ben's savings was 3 : 5. After Ali saved another $24, the ratio became 9 : 10. How much did Ali have…
- Chickens and ducks — some ducks sold at market A farm had 150 more chickens than ducks. After 90 ducks were sold at the market, the ratio of the number of ducks to the number of…
- Muffins — the apple ones stay put There were 300 more apple muffins than banana muffins in a bakery. After 150 banana muffins were sold, the ratio of the number of …
- Pens and pencils — after some pens are sold A stationery shop had 200 more pencils than pens. After 100 pens were sold, the ratio of the number of pens to the number of penci…
- Stickers — Mei and Sam's changing ratio Mei and Sam collect stickers. The ratio of Mei's stickers to Sam's stickers was 2 : 3. Mei then received 18 more stickers as a gif…
- Tank X and Tank Y held water in the ratio 7 : 9. More water was then poured into Tank X only, 4 litres worth, so the ratio became 4 : 5. How many litres did Tank X hold at first?
- The ratio of Ravi's marbles to Tom's marbles was 5 : 8. Ravi then bought 20 more marbles, so the ratio became 3 : 4. How many marbles did Ravi have at first?
- Toy cars and robots — after some robots are sold A toy store had 280 more toy cars than toy robots. After 140 toy robots were sold, the ratio of the number of toy robots to the nu…
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.