Three women, Xuan, Esther and Kimberly went on a shopping spree. 90% of Xuan's spending was equal to ¹₆ of Esther's spending. Kimberly's spending was  50% more than Esther's. If Esther spent another $1998, she would spend the same amount of money as Kimberly.

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

Xuan	Esther	Kimberly
5x2	27x2
	2x27	3x27
10 u	54 u	81 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Xuan's spending is equal to ¹₆ of Esther's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Xuan's spending = 16 of Esther's spending
910 of Xuan's spending =1x96x9 of Esther's spending
910 of Xuan's spending = 954 of Esther's spending

Xuan : Esther
10 : 54
5 : 27

Kimberly's spending in percent when compared to Esther's
= 100% + 50%
= 150%

Esther : Kimberly
100 : 150
2 : 3

Esther's spending is the repeated identity.  Make Esther's spending the same.  LCM of 27 and 2 is 54.

Xuan : Esther : Kimberly
10 : 54 : 81

(b)

	Xuan	Esther	Kimberly
Before	10 u	54 u	81 u
Change		+ 27 u
After	10 u	81 u	81 u

Additional amount that Esther would have to spend to be the same as Kimberly
= 81 u - 54 u
= 27 u

27 u = 1998

1 u = 1998 ÷ 27 = 74

Amount that Xuan spent
= 10 u
= 10 x 74
= $740 

Answer(s): (a) 10 : 54 : 81; (b) $740