Marbles — equal after a transfer
Ali had 3 times as many marbles as Ben. After Ali gave 24 marbles to Ben, the two boys had the same number of marbles. How many marbles did Ali have at first?
The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. A transfer (unlike spending) leaves the total unchanged, so "equal after" just means re-splitting that same total of units evenly — and comparing how many units one side gained or lost tells you what a single unit is worth.
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 Mrs Tan and her son — money made equal Mrs Tan had 4 times as much money as her son. After she gave him $18, the two of them had the same amount of money. How much money…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.