Three women, Marion, Usha and Mary went on a shopping spree. 90% of Marion's spending was equal to ¹₆ of Usha's spending. Mary's spending was  50% more than Usha's. If Usha spent another $2187, she would spend the same amount of money as Mary.

1. Find the ratio of Marion's spending to Usha's to Mary's.
2. How much did Marion spend?

Marion	Usha	Mary
5x2	27x2
	2x27	3x27
10 u	54 u	81 u

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

910 of Marion's spending = 16 of Usha's spending
910 of Marion's spending =1x96x9 of Usha's spending
910 of Marion's spending = 954 of Usha's spending

Marion : Usha
10 : 54
5 : 27

Mary's spending in percent when compared to Usha's
= 100% + 50%
= 150%

Usha : Mary
100 : 150
2 : 3

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

Marion : Usha : Mary
10 : 54 : 81

(b)

	Marion	Usha	Mary
Before	10 u	54 u	81 u
Change		+ 27 u
After	10 u	81 u	81 u

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

27 u = 2187

1 u = 2187 ÷ 27 = 81

Amount that Marion spent
= 10 u
= 10 x 81
= $810 

Answer(s): (a) 10 : 54 : 81; (b) $810