Three women, Usha, Jen and Wendy went on a shopping spree. 30% of Usha's spending was equal to ¹₆ of Jen's spending. Wendy's spending was  40% more than Jen's. If Jen spent another $2052, she would spend the same amount of money as Wendy.

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

Usha	Jen	Wendy
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Usha's spending is equal to ¹₆ of Jen's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Usha's spending = 16 of Jen's spending
310 of Usha's spending =1x36x3 of Jen's spending
310 of Usha's spending = 318 of Jen's spending

Usha : Jen
10 : 18
5 : 9

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

Jen : Wendy
100 : 140
5 : 7

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

Usha : Jen : Wendy
25 : 45 : 63

(b)

	Usha	Jen	Wendy
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

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

18 u = 2052

1 u = 2052 ÷ 18 = 114

Amount that Usha spent
= 25 u
= 25 x 114
= $2850 

Answer(s): (a) 25 : 45 : 63; (b) $2850