Three women, Zoe, Erika and Shiyun went on a shopping spree. 30% of Zoe's spending was equal to ¹₅ of Erika's spending. Shiyun's spending was  80% less than Erika's. If Erika spent $636 less, she would spend the same amount of money as Shiyun.

1. Find the ratio of Zoe's spending to Erika's to Shiyun's.
2. How much did Shiyun spend?

Zoe	Erika	Shiyun
2x5	3x5
	5x3	1x3
10 u	15 u	3 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Zoe's spending is equal to ¹₅ of Erika's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Zoe's spending = 15 of Erika's spending
310 of Zoe's spending =1x35x3 of Erika's spending
310 of Zoe's spending = 315 of Erika's spending

Zoe : Erika
10 : 15
2 : 3

Shiyun's spending in percent when compared to Erika's
= 100% - 80%
= 20%

Erika : Shiyun
100 : 20
5 : 1

Erika's spending is the repeated identity.  Make Erika's spending the same.  LCM of 3 and 5 is 15.

Zoe : Erika : Shiyun
10 : 15 : 3

(b)

	Zoe	Erika	Shiyun
Before	10 u	15 u	3 u
Change		- 12 u
After	10 u	3 u	3 u

Additional amount that Erika would have to spend less to be the same as Shiyun
= 15 u - 3 u
= 12 u

12 u = 636

1 u = 636 ÷ 12 = 53

Amount that Shiyun spent
= 3 u
= 3 x 53
= $159 

Answer(s): (a) 10 : 15 : 3; (b) $159