Three women, Lucy, Irene and Gillian went on a shopping spree. 30% of Lucy's spending was equal to ¹₆ of Irene's spending. Gillian's spending was  70% less than Irene's. If Irene spent $7371 less, she would spend the same amount of money as Gillian.

1. Find the ratio of Lucy's spending to Irene's to Gillian's.
2. How much did Gillian spend?

Lucy	Irene	Gillian
5x10	9x10
	10x9	3x9
50 u	90 u	27 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Lucy's spending is equal to ¹₆ of Irene's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Lucy's spending = 16 of Irene's spending
310 of Lucy's spending =1x36x3 of Irene's spending
310 of Lucy's spending = 318 of Irene's spending

Lucy : Irene
10 : 18
5 : 9

Gillian's spending in percent when compared to Irene's
= 100% - 70%
= 30%

Irene : Gillian
100 : 30
10 : 3

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

Lucy : Irene : Gillian
50 : 90 : 27

(b)

	Lucy	Irene	Gillian
Before	50 u	90 u	27 u
Change		- 63 u
After	50 u	27 u	27 u

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

63 u = 7371

1 u = 7371 ÷ 63 = 117

Amount that Gillian spent
= 27 u
= 27 x 117
= $3159 

Answer(s): (a) 50 : 90 : 27; (b) $3159