Three women, Eva, Kathy and Diana went on a shopping spree. 30% of Eva's spending was equal to ¹₅ of Kathy's spending. Diana's spending was  50% more than Kathy's. If Kathy spent another $66, she would spend the same amount of money as Diana.

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

Eva	Kathy	Diana
2x2	3x2
	2x3	3x3
4 u	6 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Eva's spending is equal to ¹₅ of Kathy's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Eva's spending = 15 of Kathy's spending
310 of Eva's spending =1x35x3 of Kathy's spending
310 of Eva's spending = 315 of Kathy's spending

Eva : Kathy
10 : 15
2 : 3

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

Kathy : Diana
100 : 150
2 : 3

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

Eva : Kathy : Diana
4 : 6 : 9

(b)

	Eva	Kathy	Diana
Before	4 u	6 u	9 u
Change		+ 3 u
After	4 u	9 u	9 u

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

3 u = 66

1 u = 66 ÷ 3 = 22

Amount that Eva spent
= 4 u
= 4 x 22
= $88 

Answer(s): (a) 4 : 6 : 9; (b) $88