Three women, Raeann, Tammy and Xylia went on a shopping spree. 30% of Raeann's spending was equal to ¹₂ of Tammy's spending. Xylia's spending was  80% less than Tammy's. If Tammy spent $432 less, she would spend the same amount of money as Xylia.

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

Raeann	Tammy	Xylia
5x5	3x5
	5x3	1x3
25 u	15 u	3 u

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

310 of Raeann's spending = 12 of Tammy's spending
310 of Raeann's spending =1x32x3 of Tammy's spending
310 of Raeann's spending = 36 of Tammy's spending

Raeann : Tammy
10 : 6
5 : 3

Xylia's spending in percent when compared to Tammy's
= 100% - 80%
= 20%

Tammy : Xylia
100 : 20
5 : 1

Tammy's spending is the repeated identity.  Make Tammy's spending the same.  LCM of 3 and 5 is 15.

Raeann : Tammy : Xylia
25 : 15 : 3

(b)

	Raeann	Tammy	Xylia
Before	25 u	15 u	3 u
Change		- 12 u
After	25 u	3 u	3 u

Additional amount that Tammy would have to spend less to be the same as Xylia
= 15 u - 3 u
= 12 u

12 u = 432

1 u = 432 ÷ 12 = 36

Amount that Xylia spent
= 3 u
= 3 x 36
= $108 

Answer(s): (a) 25 : 15 : 3; (b) $108