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18 April, 17:59

A closet containing 120 pieces of clothing is made

of sweaters, jeans, and skirts. The ratio of sweaters

to jeans is 8:3, and the ratio of jeans to skirts is

3:4. If 4 of the pairs of jeans were taken out of the

closet and were replaced by 4 skirts, what will be

the new ratio of jeans to skirts?

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Answers (1)
  1. 18 April, 18:20
    0
    5/9

    Step-by-step explanation:

    Let's define:

    sw: number of sweaters j: number of jeans sk: number of skirts

    The following three equations are established from the question:

    sw + j + sk = 120

    sw/j = 8/3

    j/sk = 3/4 or sk/j = 4/3

    Dividing the first equation by j, we get:

    sw/j + j/j + sk/j = 120/j

    8/3 + 1 + 4/3 = 120/j

    5 = 120/j

    j = 120/5 = 24

    sw = 24*8/3 = 64

    sk = 24*4/3 = 32

    After the replacement the new number of jeans and skirts are:

    j' = 24 - 4 = 20

    sk' = 32 + 4 = 36

    the new ratio of jeans to skirts is:

    j'/sk' = 20/36 = 5/9
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