Today’s problem — free all day, every step. Every day has one.
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 chickens was 1 : 4. How many chickens were there?
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There were 320 chickens.
The pattern behind it: Constant part
The ratio changes, but one person's amount stays the same.
In this one. The chickens are never sold, so the gap between the two never closes — it only grows, by exactly the 90 ducks that left, and it is that 240 the ratio has to account for.
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.
Try one like it
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…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.