Three women, Rachel, Xandra and Hazel went on a shopping spree. 70% of Rachel's spending was equal to ¹₂ of Xandra's spending. Hazel's spending was  40% less than Xandra's. If Xandra spent $770 less, she would spend the same amount of money as Hazel.

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

Rachel	Xandra	Hazel
5x5	7x5
	5x7	3x7
25 u	35 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Rachel's spending is equal to ¹₂ of Xandra's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Rachel's spending = 12 of Xandra's spending
710 of Rachel's spending =1x72x7 of Xandra's spending
710 of Rachel's spending = 714 of Xandra's spending

Rachel : Xandra
10 : 14
5 : 7

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

Xandra : Hazel
100 : 60
5 : 3

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

Rachel : Xandra : Hazel
25 : 35 : 21

(b)

	Rachel	Xandra	Hazel
Before	25 u	35 u	21 u
Change		- 14 u
After	25 u	21 u	21 u

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

14 u = 770

1 u = 770 ÷ 14 = 55

Amount that Hazel spent
= 21 u
= 21 x 55
= $1155 

Answer(s): (a) 25 : 35 : 21; (b) $1155