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? A. 3:4
B. 4:5
C. 5:9
D. 1:11

C, 5:9

Step-by-step explanation:

5/9

Step-by-step explanation:

Context for variables

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

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680