Question

Sarah and Henry share some sweets in the ratio 7:6 .

Sarah eats 12 of her sweets and the ratio of sweets left becomes 1:2 .
How many sweets did Henry have?

Answer 1

Let X be the total number of sweets.

hence, 7X/13 + 6X/13 = X.

When Sarah has eaten 12 sweets, the ratio of sweets left is, 1 : 2.

therefore,

[(7X/13) - 12] / [(6X)/13] = 1/2.

by cross multiplying, we have

14X/13 - 24 = 6X/13

14X/13 - 6X/13 = 24

8X/13 = 24; X = 39,

therefore, sarah = 7X/13 = 21

henry = 6X/13 = 18;

ratio (original) = 21:18 = 7:6

now sarah has eaten 12 sweets, balance is, 21–12=9,

sarah : henry = 9:18 = 1:2,

Henry has 18 sweets. QED
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Rooster Pomphrey

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Answer 2

Henry had 18 sweets.

(Sarah initially has 21 sweets and eats 12 of them to end up with 9 sweets.)