Three women, Emma, Xuan and Ivory went on a shopping spree. 70% of Emma's spending was equal to ¹₅ of Xuan's spending. Ivory's spending was  60% less than Xuan's. If Xuan spent $1932 less, she would spend the same amount of money as Ivory.

1. Find the ratio of Emma's spending to Xuan's to Ivory's.
2. How much did Ivory spend?

Emma	Xuan	Ivory
2x5	7x5
	5x7	2x7
10 u	35 u	14 u

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

710 of Emma's spending = 15 of Xuan's spending
710 of Emma's spending =1x75x7 of Xuan's spending
710 of Emma's spending = 735 of Xuan's spending

Emma : Xuan
10 : 35
2 : 7

Ivory's spending in percent when compared to Xuan's
= 100% - 60%
= 40%

Xuan : Ivory
100 : 40
5 : 2

Xuan's spending is the repeated identity.  Make Xuan's spending the same.  LCM of 7 and 5 is 35.

Emma : Xuan : Ivory
10 : 35 : 14

(b)

	Emma	Xuan	Ivory
Before	10 u	35 u	14 u
Change		- 21 u
After	10 u	14 u	14 u

Additional amount that Xuan would have to spend less to be the same as Ivory
= 35 u - 14 u
= 21 u

21 u = 1932

1 u = 1932 ÷ 21 = 92

Amount that Ivory spent
= 14 u
= 14 x 92
= $1288 

Answer(s): (a) 10 : 35 : 14; (b) $1288