Three women, Kylie, Gwen and Sabrina went on a shopping spree. 90% of Kylie's spending was equal to ¹₅ of Gwen's spending. Sabrina's spending was  80% less than Gwen's. If Gwen spent $3024 less, she would spend the same amount of money as Sabrina.

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

Kylie	Gwen	Sabrina
2x5	9x5
	5x9	1x9
10 u	45 u	9 u

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

910 of Kylie's spending = 15 of Gwen's spending
910 of Kylie's spending =1x95x9 of Gwen's spending
910 of Kylie's spending = 945 of Gwen's spending

Kylie : Gwen
10 : 45
2 : 9

Sabrina's spending in percent when compared to Gwen's
= 100% - 80%
= 20%

Gwen : Sabrina
100 : 20
5 : 1

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

Kylie : Gwen : Sabrina
10 : 45 : 9

(b)

	Kylie	Gwen	Sabrina
Before	10 u	45 u	9 u
Change		- 36 u
After	10 u	9 u	9 u

Additional amount that Gwen would have to spend less to be the same as Sabrina
= 45 u - 9 u
= 36 u

36 u = 3024

1 u = 3024 ÷ 36 = 84

Amount that Sabrina spent
= 9 u
= 9 x 84
= $756 

Answer(s): (a) 10 : 45 : 9; (b) $756