Same pattern as Marbles — equal after a transfer. New numbers, new
story. Try each one on paper, then check the working below — or watch it drawn out, the
same way the problem above is.
Question 1
Mei had 5 times as many stickers as Priya. After Mei gave 40 stickers to Priya, the two girls had the same number of stickers. How many stickers did Mei have at first?
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 did Mrs Tan have at first?
Ravi had 7 times as many trading cards as Zack. After Ravi gave 90 trading cards to Zack, the two boys had the same number of trading cards. How many trading cards did Ravi have at first?
Before the gift, Mei has 5 units of stickers for every 1 unit Priya has, so together they hold a fixed total.5u + u = 6u
Giving stickers away doesn't change their combined total, so afterwards the same 6 units are still shared between them, now evenly.6u ÷ 2 = 3u
Mei's share fell from 5 units to 3 units, so the units she gave away equal the stickers she handed over.5u − 3u = 2u = 40 stickers
Find what one unit is worth.u = 20 stickers
Work out how many stickers Mei had at first.5 × 20 = 100 stickers
Mei had 100 stickers at first.
The pattern. A transfer leaves the total unchanged, so 'equal after' just re-splits that fixed total, and the giver's unit-drop shows what one unit is worth — the same Constant Total pattern as the Ali and Ben problem.
Before she hands over any money, Mrs Tan has 4 units for every 1 unit her son has, so together they hold a fixed total.4u + u = 5u
Passing money to her son doesn't change their combined total, so afterwards the same 5 units are still shared between them, now evenly.5u ÷ 2 = 2.5u
Mrs Tan's share fell from 4 units to 2.5 units, so the units she gave away equal the money she handed over.4u − 2.5u = 1.5u = $18
Find what one unit is worth.u = $12
Work out how much Mrs Tan had at first.4 × $12 = $48
Mrs Tan had $48 at first.
The pattern. A transfer leaves the total unchanged, so 'equal after' just re-splits that fixed total, and the giver's unit-drop shows what one unit is worth — the same Constant Total pattern as the Ali and Ben problem.
Before trading, Ravi has 7 units of cards for every 1 unit Zack has, so together they hold a fixed total.7u + u = 8u
Handing cards to Zack doesn't change their combined total, so afterwards the same 8 units are still shared between them, now evenly.8u ÷ 2 = 4u
Ravi's share fell from 7 units to 4 units, so the units he gave away equal the cards he handed over.7u − 4u = 3u = 90 cards
Find what one unit is worth.u = 30 cards
Work out how many cards Ravi had at first.7 × 30 = 210 cards
Ravi had 210 trading cards at first.
The pattern. A transfer leaves the total unchanged, so 'equal after' just re-splits that fixed total, and the giver's unit-drop shows what one unit is worth — the same Constant Total pattern as the Ali and Ben problem.