Three women, Sarah, Nicole and Wendy went on a shopping spree. 70% of Sarah's spending was equal to ¹₅ of Nicole's spending. Wendy's spending was  25% less than Nicole's. If Nicole spent $154 less, she would spend the same amount of money as Wendy.

1. Find the ratio of Sarah's spending to Nicole's to Wendy's.
2. How much did Wendy spend?

Sarah	Nicole	Wendy
2x4	7x4
	4x7	3x7
8 u	28 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Sarah's spending is equal to ¹₅ of Nicole's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Sarah's spending = 15 of Nicole's spending
710 of Sarah's spending =1x75x7 of Nicole's spending
710 of Sarah's spending = 735 of Nicole's spending

Sarah : Nicole
10 : 35
2 : 7

Wendy's spending in percent when compared to Nicole's
= 100% - 25%
= 75%

Nicole : Wendy
100 : 75
4 : 3

Nicole's spending is the repeated identity.  Make Nicole's spending the same.  LCM of 7 and 4 is 28.

Sarah : Nicole : Wendy
8 : 28 : 21

(b)

	Sarah	Nicole	Wendy
Before	8 u	28 u	21 u
Change		- 7 u
After	8 u	21 u	21 u

Additional amount that Nicole would have to spend less to be the same as Wendy
= 28 u - 21 u
= 7 u

7 u = 154

1 u = 154 ÷ 7 = 22

Amount that Wendy spent
= 21 u
= 21 x 22
= $462 

Answer(s): (a) 8 : 28 : 21; (b) $462