Today’s problem — free all day, every step. Every day has one.
John's money — T-shirt, shoes, and $120 from his parents
At first, John had some money. He spent of it on a T-shirt and of the remainder on a pair of shoes. After that, his parents gave him $120. The ratio of the total amount of money he had at the end to the amount of money he had at first was 5 : 4. How much did John have at first?
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65 worked examples are free without a code, two from every pattern. No account, either way.
The pattern behind it: Branching
The second fraction is of one piece, not of the whole.
In this one. Cut the starting amount into 20 equal units so that both cuts (1/4, then 2/5 of what is left) land on whole boxes; the ratio 5 : 4 then measures the end amount in those same units — 25 of them — so the $120 can only be the gap, 25u - 9u = 16u.
How to spot it
A second fraction arrives after the first and is attached to a piece rather than to the whole — 'of the remainder', 'of what was left', or 'of the ones that were red'.
Common mistake
Children take the second fraction of the original total instead of the piece it was named against, which makes the amount come out too big.
Try one like it
Challenging Piggy bank — a video game, headphones, and an uncle's gift Ravi had some money saved in his piggy bank. He spent 1/4 of it on a video game and 2/5 of the remainder on a pair of headphones. …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.