Three women, Esther, Winnie and Min went on a shopping spree. 90% of Esther's spending was equal to ¹₂ of Winnie's spending. Min's spending was  40% more than Winnie's. If Winnie spent another $1242, she would spend the same amount of money as Min.

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

Esther	Winnie	Min
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

910 of Esther's spending = 12 of Winnie's spending
910 of Esther's spending =1x92x9 of Winnie's spending
910 of Esther's spending = 918 of Winnie's spending

Esther : Winnie
10 : 18
5 : 9

Min's spending in percent when compared to Winnie's
= 100% + 40%
= 140%

Winnie : Min
100 : 140
5 : 7

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

Esther : Winnie : Min
25 : 45 : 63

(b)

	Esther	Winnie	Min
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

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

18 u = 1242

1 u = 1242 ÷ 18 = 69

Amount that Esther spent
= 25 u
= 25 x 69
= $1725 

Answer(s): (a) 25 : 45 : 63; (b) $1725