Three women, Mary, Hilda and Rachel went on a shopping spree. 30% of Mary's spending was equal to ¹₅ of Hilda's spending. Rachel's spending was  25% less than Hilda's. If Hilda spent $111 less, she would spend the same amount of money as Rachel.

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

Mary	Hilda	Rachel
2x4	3x4
	4x3	3x3
8 u	12 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Mary's spending is equal to ¹₅ of Hilda's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Mary's spending = 15 of Hilda's spending
310 of Mary's spending =1x35x3 of Hilda's spending
310 of Mary's spending = 315 of Hilda's spending

Mary : Hilda
10 : 15
2 : 3

Rachel's spending in percent when compared to Hilda's
= 100% - 25%
= 75%

Hilda : Rachel
100 : 75
4 : 3

Hilda's spending is the repeated identity.  Make Hilda's spending the same.  LCM of 3 and 4 is 12.

Mary : Hilda : Rachel
8 : 12 : 9

(b)

	Mary	Hilda	Rachel
Before	8 u	12 u	9 u
Change		- 3 u
After	8 u	9 u	9 u

Additional amount that Hilda would have to spend less to be the same as Rachel
= 12 u - 9 u
= 3 u

3 u = 111

1 u = 111 ÷ 3 = 37

Amount that Rachel spent
= 9 u
= 9 x 37
= $333 

Answer(s): (a) 8 : 12 : 9; (b) $333