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Question P6 Constant total

Today’s problem — free all day, every step. Every day has one.

Chocolates — all three end equal

Alina, Betty and Cindy shared some chocolates. Alina had of the total, Betty had 25% as many as Cindy, and Cindy gave 104 chocolates to the other two so that all three had equal amounts. Find the original total.

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About this method

Constant total

Money moves between two people, so their total never changes.

In this one. When the unchanged total must be shared equally among 3 people, scale the starting ratio so its total number of units is divisible by 3.

Before4 shares in allAlithis one movesBenAfter4 shares in allAliBenarrived here

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.

Practise a similar question

Standard 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 : 7. Together they had 144 cards throughout. How many cards did Liam give to Noah?
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