Three women, Xylia, Jane and Kimberly went on a shopping spree. 90% of Xylia's spending was equal to ¹₂ of Jane's spending. Kimberly's spending was  60% less than Jane's. If Jane spent $2133 less, she would spend the same amount of money as Kimberly.

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

Xylia	Jane	Kimberly
5x5	9x5
	5x9	2x9
25 u	45 u	18 u

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

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

Xylia : Jane
10 : 18
5 : 9

Kimberly's spending in percent when compared to Jane's
= 100% - 60%
= 40%

Jane : Kimberly
100 : 40
5 : 2

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

Xylia : Jane : Kimberly
25 : 45 : 18

(b)

	Xylia	Jane	Kimberly
Before	25 u	45 u	18 u
Change		- 27 u
After	25 u	18 u	18 u

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

27 u = 2133

1 u = 2133 ÷ 27 = 79

Amount that Kimberly spent
= 18 u
= 18 x 79
= $1422 

Answer(s): (a) 25 : 45 : 18; (b) $1422