Three women, Wendy, Usha and Kimberly went on a shopping spree. 30% of Wendy's spending was equal to ¹₂ of Usha's spending. Kimberly's spending was  70% less than Usha's. If Usha spent $819 less, she would spend the same amount of money as Kimberly.

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

Wendy	Usha	Kimberly
5x10	3x10
	10x3	3x3
50 u	30 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Wendy's spending is equal to ¹₂ of Usha's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Wendy's spending = 12 of Usha's spending
310 of Wendy's spending =1x32x3 of Usha's spending
310 of Wendy's spending = 36 of Usha's spending

Wendy : Usha
10 : 6
5 : 3

Kimberly's spending in percent when compared to Usha's
= 100% - 70%
= 30%

Usha : Kimberly
100 : 30
10 : 3

Usha's spending is the repeated identity.  Make Usha's spending the same.  LCM of 3 and 10 is 30.

Wendy : Usha : Kimberly
50 : 30 : 9

(b)

	Wendy	Usha	Kimberly
Before	50 u	30 u	9 u
Change		- 21 u
After	50 u	9 u	9 u

Additional amount that Usha would have to spend less to be the same as Kimberly
= 30 u - 9 u
= 21 u

21 u = 819

1 u = 819 ÷ 21 = 39

Amount that Kimberly spent
= 9 u
= 9 x 39
= $351 

Answer(s): (a) 50 : 30 : 9; (b) $351