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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?

 Aug 4, 2023
edited by JCase8904  Aug 4, 2023
 #1
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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

 

 

cool cool cool

 Aug 4, 2023

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