Three women, Risa, Sabrina and Wendy went on a shopping spree. 90% of Risa's spending was equal to ¹₅ of Sabrina's spending. Wendy's spending was  40% less than Sabrina's. If Sabrina spent $414 less, she would spend the same amount of money as Wendy.

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

Risa	Sabrina	Wendy
2x5	9x5
	5x9	3x9
10 u	45 u	27 u

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

910 of Risa's spending = 15 of Sabrina's spending
910 of Risa's spending =1x95x9 of Sabrina's spending
910 of Risa's spending = 945 of Sabrina's spending

Risa : Sabrina
10 : 45
2 : 9

Wendy's spending in percent when compared to Sabrina's
= 100% - 40%
= 60%

Sabrina : Wendy
100 : 60
5 : 3

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

Risa : Sabrina : Wendy
10 : 45 : 27

(b)

	Risa	Sabrina	Wendy
Before	10 u	45 u	27 u
Change		- 18 u
After	10 u	27 u	27 u

Additional amount that Sabrina would have to spend less to be the same as Wendy
= 45 u - 27 u
= 18 u

18 u = 414

1 u = 414 ÷ 18 = 23

Amount that Wendy spent
= 27 u
= 27 x 23
= $621 

Answer(s): (a) 10 : 45 : 27; (b) $621