Three women, Ivory, Hazel and Yen went on a shopping spree. 70% of Ivory's spending was equal to ¹₅ of Hazel's spending. Yen's spending was  60% less than Hazel's. If Hazel spent $1008 less, she would spend the same amount of money as Yen.

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

Ivory	Hazel	Yen
2x5	7x5
	5x7	2x7
10 u	35 u	14 u

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

710 of Ivory's spending = 15 of Hazel's spending
710 of Ivory's spending =1x75x7 of Hazel's spending
710 of Ivory's spending = 735 of Hazel's spending

Ivory : Hazel
10 : 35
2 : 7

Yen's spending in percent when compared to Hazel's
= 100% - 60%
= 40%

Hazel : Yen
100 : 40
5 : 2

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

Ivory : Hazel : Yen
10 : 35 : 14

(b)

	Ivory	Hazel	Yen
Before	10 u	35 u	14 u
Change		- 21 u
After	10 u	14 u	14 u

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

21 u = 1008

1 u = 1008 ÷ 21 = 48

Amount that Yen spent
= 14 u
= 14 x 48
= $672 

Answer(s): (a) 10 : 35 : 14; (b) $672