Today’s problem — free all day, every step. Every day has one.
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 were in the club at first?
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9 boys (and 12 girls at first).
The pattern behind it: Everything changed
Both amounts change, so no total and no gap stays fixed.
In this one. Both sides changed, so neither the total nor the difference stays fixed — write the end state in the same units as the start, and let the new ratio pin what one unit is worth.
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.