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28 August, 13:53

Sarah and Henry share some sweets in the ratio 5:6. Sarah eats 16 of their sweets and the ratio of sweets left becomes 1:2. How many sweets did Henry have?

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  1. 28 August, 17:28
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    Answer: 48 sweets

    Step-by-step explanation:

    Let the total number of sweets be X

    Thereforee, 5X/11 + 6X/11 = X.

    When Sarah ate 16 sweets, the ratio of sweets left is 1 : 2.

    [ (5X/11) - 16] / [6X/11] = 1/2.

    Cross multiply,

    10X/11 - 32 = 6X/11

    10X/11 - 6X/11 = 32

    4X/11 = 32

    4X = 32 * 11

    4X = 352

    X = 352/4

    X = 88

    therefore, sarah = 5X/11

    = (5 * 88) : 11 = 440/11 = 40

    Henry = 6X/11

    = (6 * 88) : 11

    = 48

    Therefore, the original ratio was:

    5 : 6 = 40 : 48

    Sarah ate 16 sweets, her balance is:

    40 - 16 = 24

    Sarah : Henry = 24:48 = 1:2

    Henry has 48 sweets.
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