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Emma and Lily's savings — 2 : 1 becomes 4 : 1
The ratio of Emma’s savings to Lily’s savings was 2:1. After Emma saved $60 and Lily spent $30, the new ratio became 4:1. How much money did Emma have at first?
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The pattern behind it: Everything changed
Both amounts change, so no total and no gap stays fixed.
In this one. Both quantities changed, so a unit of the ratio at first and a part of the ratio at the end are different sizes — swap every unit for 1 part + 30 (Lily's change) and Emma's whole equation becomes one in parts alone.
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 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…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.