Audrey had 40% more coins than Kaylee. Zoe had 20% fewer coins than Audrey. Audrey and Kaylee gave Zoe some coins in the ratio of 3 : 4. As a result, Zoe had 50% more coins than before. Given that Zoe had 175 more coins than Kaylee in the end, how many coins did Audrey give to Zoe?

Audrey	Kaylee	Zoe
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Audrey : Kaylee = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Audrey : Zoe = 5 : 4

The number of coins that Audrey had at first is repeated. Make the number of coins that Audrey had at first the same.  LCM of 7 and 5 is 35.

	Audrey	Kaylee	Zoe
Before	35x1 =  35 u	25x1 = 25 u	28x1 = 28 u
Change			+ 14x1 = + 14 u
Comparing the changes in the number of coins	- 3x2 = - 6 u	- 4x2 = - 8 u	+ 7x2 = + 14 u
After	29 u	17 u	42x1 = 42 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of coins that Audrey and Kaylee gave to Zoe is repeated.  Make the total number of coins that Audrey and Kaylee gave to Zoe the same.  LCM of 7 and 14 is 14.

Number of coins that Zoe had more than Kaylee 
= 42 u - 17 u
= 25 u

25 u = 175

1 u = 175 ÷ 25 = 7

Number of coins that Audrey gave to Zoe
= 6 u
= 6 x 7
= 42

Answer(s): 42