There are 3 shoes racks in a shop. Rack A has 40% as many pairs of shoes as Rack B and Rack C. The total number of pairs of shoes in Rack A and Rack C is 75% as many as Rack B. After moving 42 pairs of shoes from Rack B to Rack A, both Rack B and A now has an equal number of pairs of shoes. How many pairs of shoes are there altogether in the 3 racks?

JCase8904 Aug 4, 2023

#1**+1 **

Before the transfer from B to A let the number of shoes in each rack = A, B and C

We have these equations

A = .40(B + C) → C = A /.40 - B (1)

.75B = (A + C) → C = .75B - A (2)

Equate (1) and (2)

A/.40 - B = .75B - A

A/.40 + A = .75B + B

2.5A + A = 1.75B

3.5A = 1.75B (1)

After the transfer

A + 42 = B - 42 simplify

A = B - 84 (2)

Sub (2) into (1)

3.5 ( B - 84) = 1.75B

3.5B - 294 = 1.75B

3.5B - 1.75B = 294

1.75B = 294

B = 294/1.75 = 168

A = B - 84 = 168 - 84 = 84

C = .75B - A = .75 (168) - 84 = 42

So the total number of shoes = 168 + 84 + 42 = 294

CPhill Aug 4, 2023