Three women, Cathy, Eva and Xylia went on a shopping spree. 30% of Cathy's spending was equal to ¹₂ of Eva's spending. Xylia's spending was  50% more than Eva's. If Eva spent another $258, she would spend the same amount of money as Xylia.

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

Cathy	Eva	Xylia
5x2	3x2
	2x3	3x3
10 u	6 u	9 u

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

310 of Cathy's spending = 12 of Eva's spending
310 of Cathy's spending =1x32x3 of Eva's spending
310 of Cathy's spending = 36 of Eva's spending

Cathy : Eva
10 : 6
5 : 3

Xylia's spending in percent when compared to Eva's
= 100% + 50%
= 150%

Eva : Xylia
100 : 150
2 : 3

Eva's spending is the repeated identity.  Make Eva's spending the same.  LCM of 3 and 2 is 6.

Cathy : Eva : Xylia
10 : 6 : 9

(b)

	Cathy	Eva	Xylia
Before	10 u	6 u	9 u
Change		+ 3 u
After	10 u	9 u	9 u

Additional amount that Eva would have to spend to be the same as Xylia
= 9 u - 6 u
= 3 u

3 u = 258

1 u = 258 ÷ 3 = 86

Amount that Cathy spent
= 10 u
= 10 x 86
= $860 

Answer(s): (a) 10 : 6 : 9; (b) $860