Three women, Hazel, Usha and Rachel went on a shopping spree. 90% of Hazel's spending was equal to ¹₂ of Usha's spending. Rachel's spending was  70% less than Usha's. If Usha spent $2520 less, she would spend the same amount of money as Rachel.

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

Hazel	Usha	Rachel
5x10	9x10
	10x9	3x9
50 u	90 u	27 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Hazel's spending is equal to ¹₂ of Usha's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Hazel's spending = 12 of Usha's spending
910 of Hazel's spending =1x92x9 of Usha's spending
910 of Hazel's spending = 918 of Usha's spending

Hazel : Usha
10 : 18
5 : 9

Rachel's spending in percent when compared to Usha's
= 100% - 70%
= 30%

Usha : Rachel
100 : 30
10 : 3

Usha's spending is the repeated identity.  Make Usha's spending the same.  LCM of 9 and 10 is 90.

Hazel : Usha : Rachel
50 : 90 : 27

(b)

	Hazel	Usha	Rachel
Before	50 u	90 u	27 u
Change		- 63 u
After	50 u	27 u	27 u

Additional amount that Usha would have to spend less to be the same as Rachel
= 90 u - 27 u
= 63 u

63 u = 2520

1 u = 2520 ÷ 63 = 40

Amount that Rachel spent
= 27 u
= 27 x 40
= $1080 

Answer(s): (a) 50 : 90 : 27; (b) $1080