Three women, Kimberly, Roshel and Zoe went on a shopping spree. 90% of Kimberly's spending was equal to ¹₅ of Roshel's spending. Zoe's spending was  40% more than Roshel's. If Roshel spent another $1998, she would spend the same amount of money as Zoe.

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

Kimberly	Roshel	Zoe
2x5	9x5
	5x9	7x9
10 u	45 u	63 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Kimberly's spending is equal to ¹₅ of Roshel's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Kimberly's spending = 15 of Roshel's spending
910 of Kimberly's spending =1x95x9 of Roshel's spending
910 of Kimberly's spending = 945 of Roshel's spending

Kimberly : Roshel
10 : 45
2 : 9

Zoe's spending in percent when compared to Roshel's
= 100% + 40%
= 140%

Roshel : Zoe
100 : 140
5 : 7

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

Kimberly : Roshel : Zoe
10 : 45 : 63

(b)

	Kimberly	Roshel	Zoe
Before	10 u	45 u	63 u
Change		+ 18 u
After	10 u	63 u	63 u

Additional amount that Roshel would have to spend to be the same as Zoe
= 63 u - 45 u
= 18 u

18 u = 1998

1 u = 1998 ÷ 18 = 111

Amount that Kimberly spent
= 10 u
= 10 x 111
= $1110 

Answer(s): (a) 10 : 45 : 63; (b) $1110