Three women, Hazel, Abi and Min went on a shopping spree. 90% of Hazel's spending was equal to ¹₆ of Abi's spending. Min's spending was  70% less than Abi's. If Abi spent $7560 less, she would spend the same amount of money as Min.

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

Hazel	Abi	Min
5x10	27x10
	10x27	3x27
50 u	270 u	81 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Hazel's spending is equal to ¹₆ of Abi's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Hazel's spending = 16 of Abi's spending
910 of Hazel's spending =1x96x9 of Abi's spending
910 of Hazel's spending = 954 of Abi's spending

Hazel : Abi
10 : 54
5 : 27

Min's spending in percent when compared to Abi's
= 100% - 70%
= 30%

Abi : Min
100 : 30
10 : 3

Abi's spending is the repeated identity.  Make Abi's spending the same.  LCM of 27 and 10 is 270.

Hazel : Abi : Min
50 : 270 : 81

(b)

	Hazel	Abi	Min
Before	50 u	270 u	81 u
Change		- 189 u
After	50 u	81 u	81 u

Additional amount that Abi would have to spend less to be the same as Min
= 270 u - 81 u
= 189 u

189 u = 7560

1 u = 7560 ÷ 189 = 40

Amount that Min spent
= 81 u
= 81 x 40
= $3240 

Answer(s): (a) 50 : 270 : 81; (b) $3240