Three women, Abi, Eva and Victoria went on a shopping spree. 90% of Abi's spending was equal to ¹₅ of Eva's spending. Victoria's spending was  60% more than Eva's. If Eva spent another $567, she would spend the same amount of money as Victoria.

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

Abi	Eva	Victoria
2x5	9x5
	5x9	8x9
10 u	45 u	72 u

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

910 of Abi's spending = 15 of Eva's spending
910 of Abi's spending =1x95x9 of Eva's spending
910 of Abi's spending = 945 of Eva's spending

Abi : Eva
10 : 45
2 : 9

Victoria's spending in percent when compared to Eva's
= 100% + 60%
= 160%

Eva : Victoria
100 : 160
5 : 8

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

Abi : Eva : Victoria
10 : 45 : 72

(b)

	Abi	Eva	Victoria
Before	10 u	45 u	72 u
Change		+ 27 u
After	10 u	72 u	72 u

Additional amount that Eva would have to spend to be the same as Victoria
= 72 u - 45 u
= 27 u

27 u = 567

1 u = 567 ÷ 27 = 21

Amount that Abi spent
= 10 u
= 10 x 21
= $210 

Answer(s): (a) 10 : 45 : 72; (b) $210