Question P6 Constant total
Today’s problem — free all day, every step. Every day has one.
The ratio of cookies in Box A to cookies in Box B was 5 : 3. After 16 cookies were moved from Box A to Box B, the ratio became 3 : 5. How many cookies were in Box A at first?
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Money moves between two people, so their total never changes.
In this one. Both ratios add up to 8 shares, and no cookies entered or left, so the total is the same 8 shares before and after — which forces 1 part (after) to be exactly 1 unit (before), and the 16 cookies to be exactly 2 units.
One person gives, sells or loses an amount to the other, and nobody outside the two people gains or loses anything.
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.
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