Three women, Winnie, Pamela and Raeann went on a shopping spree. 90% of Winnie's spending was equal to ¹₅ of Pamela's spending. Raeann's spending was  40% more than Pamela's. If Pamela spent another $378, she would spend the same amount of money as Raeann.

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

Winnie	Pamela	Raeann
2x5	9x5
	5x9	7x9
10 u	45 u	63 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Winnie's spending is equal to ¹₅ of Pamela's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Winnie's spending = 15 of Pamela's spending
910 of Winnie's spending =1x95x9 of Pamela's spending
910 of Winnie's spending = 945 of Pamela's spending

Winnie : Pamela
10 : 45
2 : 9

Raeann's spending in percent when compared to Pamela's
= 100% + 40%
= 140%

Pamela : Raeann
100 : 140
5 : 7

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

Winnie : Pamela : Raeann
10 : 45 : 63

(b)

	Winnie	Pamela	Raeann
Before	10 u	45 u	63 u
Change		+ 18 u
After	10 u	63 u	63 u

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

18 u = 378

1 u = 378 ÷ 18 = 21

Amount that Winnie spent
= 10 u
= 10 x 21
= $210 

Answer(s): (a) 10 : 45 : 63; (b) $210