Today’s problem — free all day, every step. Every day has one.
Ken and Mei's piggy banks held money in the ratio 3 : 1.
Ken and Mei's piggy banks held money in the ratio 3 : 1. After Ken transferred $30 to Mei's piggy bank, the ratio became 1 : 3. How much money did Ken have at first?
Show the answerHide the answer
See all 6 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 a free one like it
65 worked examples are free without a code, two from every pattern. No account, either way.
The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. Because a transfer keeps the combined total fixed, the same total of 4 parts before and after means each part has the same value, so Ken's drop from 3 parts to 1 part is exactly the $30 transferred.
How to spot it
One person gives, sells or loses an amount to the other, and nobody outside the two people gains or loses anything.
Common mistake
Children draw different totals before and after, or forget that moving an amount from one person to the other changes the gap between them by twice that amount.
Try one like it
Standard Liam and Noah's cards — 7 : 5 becomes 5 : 7 The ratio of Liam's trading cards to Noah's trading cards was 7 : 5. After Liam gave some of his cards to Noah, the ratio became 5…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.