Today’s problem — free all day, every step. Every day has one.
Savings — a novel, a backpack, and grandmother's gift
Mei had some savings. She spent of it on a novel and of the remainder on a backpack. After that, her grandmother gave her $160. The ratio of the total amount she had at the end to the amount she had at first was 5 : 4. How much did Mei have at first?
Show the answerHide the answer
See all 12 steps
MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
I have a code → See the free ones
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 units — 4 × 5 — so that the quarter, the fifths of the remainder, and the 5 : 4 ratio all land on whole boxes; the $160 gift then shows up as a clean gap of 16 units.
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 John's money — T-shirt, shoes, and $120 from his parents At first, John had some money. He spent 1/4 of it on a T-shirt and 2/5 of the remainder on a pair of shoes. After that, his parent…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.