The pattern
Everything changed
Both amounts change, so no total and no gap stays fixed.
Both people change, one by saving or gaining, the other by spending or losing, so neither their total nor the gap between them stays fixed. Draw the after amounts in shares the same size as the before ones, add or take away what changed, and the ratio after tells you what one share before 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.
7 worked solutions
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…
- 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 …
- 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…
- Marbles — Marcus and Ben's game The ratio of Marcus's marble collection to Ben's marble collection was 3:2. After Marcus won 24 more marbles and Ben lost 9 marble…
- Mrs Tan and Mrs Lee's stamps — 2 : 1 to 4 : 1 The number of stamps Mrs Tan owned to the number Mrs Lee owned was in the ratio 2 : 1. After Mrs Tan received another 180 stamps a…
- Ravi and Suresh's marbles — 2 : 1 to 4 : 1 The number of marbles Ravi had to the number Suresh had was in the ratio 2 : 1. After Ravi won another 200 marbles and Suresh lost…
- The ratio of Aisha's savings to Mei's savings was 3:1. After Aisha saved $40 more and Mei spent $10, the new ratio became 5:1. How much money did Aisha have at first?
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.