Three women, Erika, Vanessa and Shiyun went on a shopping spree. 70% of Erika's spending was equal to ¹₆ of Vanessa's spending. Shiyun's spending was  70% less than Vanessa's. If Vanessa spent $11172 less, she would spend the same amount of money as Shiyun.

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

Erika	Vanessa	Shiyun
5x10	21x10
	10x21	3x21
50 u	210 u	63 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Erika's spending is equal to ¹₆ of Vanessa's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Erika's spending = 16 of Vanessa's spending
710 of Erika's spending =1x76x7 of Vanessa's spending
710 of Erika's spending = 742 of Vanessa's spending

Erika : Vanessa
10 : 42
5 : 21

Shiyun's spending in percent when compared to Vanessa's
= 100% - 70%
= 30%

Vanessa : Shiyun
100 : 30
10 : 3

Vanessa's spending is the repeated identity.  Make Vanessa's spending the same.  LCM of 21 and 10 is 210.

Erika : Vanessa : Shiyun
50 : 210 : 63

(b)

	Erika	Vanessa	Shiyun
Before	50 u	210 u	63 u
Change		- 147 u
After	50 u	63 u	63 u

Additional amount that Vanessa would have to spend less to be the same as Shiyun
= 210 u - 63 u
= 147 u

147 u = 11172

1 u = 11172 ÷ 147 = 76

Amount that Shiyun spent
= 63 u
= 63 x 76
= $4788 

Answer(s): (a) 50 : 210 : 63; (b) $4788