Three women, Rachel, Hilda and Raeann went on a shopping spree. 70% of Rachel's spending was equal to ¹₂ of Hilda's spending. Raeann's spending was  25% more than Hilda's. If Hilda spent another $168, she would spend the same amount of money as Raeann.

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

Rachel	Hilda	Raeann
5x4	7x4
	4x7	5x7
20 u	28 u	35 u

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

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

Rachel : Hilda
10 : 14
5 : 7

Raeann's spending in percent when compared to Hilda's
= 100% + 25%
= 125%

Hilda : Raeann
100 : 125
4 : 5

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

Rachel : Hilda : Raeann
20 : 28 : 35

(b)

	Rachel	Hilda	Raeann
Before	20 u	28 u	35 u
Change		+ 7 u
After	20 u	35 u	35 u

Additional amount that Hilda would have to spend to be the same as Raeann
= 35 u - 28 u
= 7 u

7 u = 168

1 u = 168 ÷ 7 = 24

Amount that Rachel spent
= 20 u
= 20 x 24
= $480 

Answer(s): (a) 20 : 28 : 35; (b) $480