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Ali and Billy — 2 : 1 becomes 4 : 1
The ratio of Ali’s money to Billy’s money was 2 : 1. After Ali saved another $60 and Billy spent $150, the ratio became 4 : 1. How much money did Ali have at first?
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Ali had $660 at first. (Billy had $330.)
The pattern behind it: Everything changed
Both amounts change, so no total and no gap stays fixed.
In this one. Ali's money in the end has two names — 2 units + $60 (from the ratio at first) and 4 units − $600 (because it is 4 copies of Billy's end amount, 1 unit − $150); setting the two names side by side and cancelling the units they share turns the picture into a number.
How to spot it
Both people in a ratio change by different amounts, with words like 'joined' or 'saved more' for one and 'left' or 'spent' for the other.
Common mistake
Children look for a fixed total or a fixed gap out of habit. Neither is fixed here, so only the ratio at the end can give the size of a share.
Try one like it
Challenging Chess club — boys join, girls leave The ratio of boys to girls in a chess club was 3 : 4. After 6 boys joined and 2 girls left, the ratio became 3 : 2. How many boys …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.