Three women, Lucy, Wendy and Esther went on a shopping spree. 90% of Lucy's spending was equal to ¹₂ of Wendy's spending. Esther's spending was  40% more than Wendy's. If Wendy spent another $630, she would spend the same amount of money as Esther.

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

Lucy	Wendy	Esther
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

910 of Lucy's spending = 12 of Wendy's spending
910 of Lucy's spending =1x92x9 of Wendy's spending
910 of Lucy's spending = 918 of Wendy's spending

Lucy : Wendy
10 : 18
5 : 9

Esther's spending in percent when compared to Wendy's
= 100% + 40%
= 140%

Wendy : Esther
100 : 140
5 : 7

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

Lucy : Wendy : Esther
25 : 45 : 63

(b)

	Lucy	Wendy	Esther
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

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

18 u = 630

1 u = 630 ÷ 18 = 35

Amount that Lucy spent
= 25 u
= 25 x 35
= $875 

Answer(s): (a) 25 : 45 : 63; (b) $875