Three women, Eva, Xylia and Kathy went on a shopping spree. 70% of Eva's spending was equal to ¹₅ of Xylia's spending. Kathy's spending was  50% more than Xylia's. If Xylia spent another $399, she would spend the same amount of money as Kathy.

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

Eva	Xylia	Kathy
2x2	7x2
	2x7	3x7
4 u	14 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Eva's spending is equal to ¹₅ of Xylia's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Eva's spending = 15 of Xylia's spending
710 of Eva's spending =1x75x7 of Xylia's spending
710 of Eva's spending = 735 of Xylia's spending

Eva : Xylia
10 : 35
2 : 7

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

Xylia : Kathy
100 : 150
2 : 3

Xylia's spending is the repeated identity.  Make Xylia's spending the same.  LCM of 7 and 2 is 14.

Eva : Xylia : Kathy
4 : 14 : 21

(b)

	Eva	Xylia	Kathy
Before	4 u	14 u	21 u
Change		+ 7 u
After	4 u	21 u	21 u

Additional amount that Xylia would have to spend to be the same as Kathy
= 21 u - 14 u
= 7 u

7 u = 399

1 u = 399 ÷ 7 = 57

Amount that Eva spent
= 4 u
= 4 x 57
= $228 

Answer(s): (a) 4 : 14 : 21; (b) $228