Question

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?​

Answer 1

5/9

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