Three women, Jane, Elyse and Shiyun went on a shopping spree. 90% of Jane's spending was equal to ¹₂ of Elyse's spending. Shiyun's spending was  50% more than Elyse's. If Elyse spent another $792, she would spend the same amount of money as Shiyun.

1. Find the ratio of Jane's spending to Elyse's to Shiyun's.
2. How much did Jane spend?

Jane	Elyse	Shiyun
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

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

910 of Jane's spending = 12 of Elyse's spending
910 of Jane's spending =1x92x9 of Elyse's spending
910 of Jane's spending = 918 of Elyse's spending

Jane : Elyse
10 : 18
5 : 9

Shiyun's spending in percent when compared to Elyse's
= 100% + 50%
= 150%

Elyse : Shiyun
100 : 150
2 : 3

Elyse's spending is the repeated identity.  Make Elyse's spending the same.  LCM of 9 and 2 is 18.

Jane : Elyse : Shiyun
10 : 18 : 27

(b)

	Jane	Elyse	Shiyun
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

Additional amount that Elyse would have to spend to be the same as Shiyun
= 27 u - 18 u
= 9 u

9 u = 792

1 u = 792 ÷ 9 = 88

Amount that Jane spent
= 10 u
= 10 x 88
= $880 

Answer(s): (a) 10 : 18 : 27; (b) $880