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17 October, 01:01

The ratio of the number of Mimi's Eminem cd's to the number of Rita's Eminem cd's is 5:8. Rita has 18 more Eminem cd's than Mimi. If Rita gives 22cd's to Mimi, what will be the new ratio of the number of Mimi's Eminem cd's to Rita's?

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  1. 17 October, 04:56
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    M = Mimi’s cd’s

    R = Rita’s cd’s

    The ratio of the number of Mimi’s Eminem cd’s to the number of Rita’s Eminem cd’s is 5:8 mean:

    M / R = 5 / 8

    Rita has 18 more Eminem cd’s than Mimi mean:

    R = M + 18

    Now you have system of 2 equations with 2 unknow.

    M / R = 5 / 8 and R = M + 18

    M / R = 5 / 8 Multiply both sides by R

    M = 5 R / 8 Multiply both sides by 8

    8 M = 5 R

    Your system become:

    R = M + 18

    8 M = 5 R

    Replace R = M + 18 into equation 8 M = 5 R

    8 M = 5 (M + 18)

    8 M = 5 M + 5 * 18

    8 M = 5 M + 90 Subtract 5 M to both sides

    8 M - 5 M = 5 M + 90 - 5 M

    3 M = 90 Divide both sides by 3

    M = 90 / 3

    M = 30

    Mimi has 30 cd’s

    Rita has:

    R = M + 18 = 30 + 18 = 48

    R = 48

    Rita has 48 cd’s

    If Rita gives 22cd’s to Mimi she will have 48 - 22 = 26 cd

    Mimi will have 30 + 22 = 52 cd

    The new ratio of the number of Mimi’s cd’s to Rita’s cd’s will be:

    M / R = 26 / 52 = 26 / 2 * 26 = 1:2
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