Three women, Natalie, Zoe and Kylie went on a shopping spree. 30% of Natalie's spending was equal to ¹₂ of Zoe's spending. Kylie's spending was  60% less than Zoe's. If Zoe spent $1026 less, she would spend the same amount of money as Kylie.

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

Natalie	Zoe	Kylie
5x5	3x5
	5x3	2x3
25 u	15 u	6 u

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

310 of Natalie's spending = 12 of Zoe's spending
310 of Natalie's spending =1x32x3 of Zoe's spending
310 of Natalie's spending = 36 of Zoe's spending

Natalie : Zoe
10 : 6
5 : 3

Kylie's spending in percent when compared to Zoe's
= 100% - 60%
= 40%

Zoe : Kylie
100 : 40
5 : 2

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

Natalie : Zoe : Kylie
25 : 15 : 6

(b)

	Natalie	Zoe	Kylie
Before	25 u	15 u	6 u
Change		- 9 u
After	25 u	6 u	6 u

Additional amount that Zoe would have to spend less to be the same as Kylie
= 15 u - 6 u
= 9 u

9 u = 1026

1 u = 1026 ÷ 9 = 114

Amount that Kylie spent
= 6 u
= 6 x 114
= $684 

Answer(s): (a) 25 : 15 : 6; (b) $684