Three women, Ivory, Shannon and Zoe went on a shopping spree. 30% of Ivory's spending was equal to ¹₆ of Shannon's spending. Zoe's spending was  60% less than Shannon's. If Shannon spent $2187 less, she would spend the same amount of money as Zoe.

1. Find the ratio of Ivory's spending to Shannon's to Zoe's.
2. How much did Zoe spend?

Ivory	Shannon	Zoe
5x5	9x5
	5x9	2x9
25 u	45 u	18 u

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

310 of Ivory's spending = 16 of Shannon's spending
310 of Ivory's spending =1x36x3 of Shannon's spending
310 of Ivory's spending = 318 of Shannon's spending

Ivory : Shannon
10 : 18
5 : 9

Zoe's spending in percent when compared to Shannon's
= 100% - 60%
= 40%

Shannon : Zoe
100 : 40
5 : 2

Shannon's spending is the repeated identity.  Make Shannon's spending the same.  LCM of 9 and 5 is 45.

Ivory : Shannon : Zoe
25 : 45 : 18

(b)

	Ivory	Shannon	Zoe
Before	25 u	45 u	18 u
Change		- 27 u
After	25 u	18 u	18 u

Additional amount that Shannon would have to spend less to be the same as Zoe
= 45 u - 18 u
= 27 u

27 u = 2187

1 u = 2187 ÷ 27 = 81

Amount that Zoe spent
= 18 u
= 18 x 81
= $1458 

Answer(s): (a) 25 : 45 : 18; (b) $1458