Three women, Eva, Opal and Victoria went on a shopping spree. 90% of Eva's spending was equal to ¹₅ of Opal's spending. Victoria's spending was  25% more than Opal's. If Opal spent another $315, she would spend the same amount of money as Victoria.

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

Eva	Opal	Victoria
2x4	9x4
	4x9	5x9
8 u	36 u	45 u

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

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

Eva : Opal
10 : 45
2 : 9

Victoria's spending in percent when compared to Opal's
= 100% + 25%
= 125%

Opal : Victoria
100 : 125
4 : 5

Opal's spending is the repeated identity.  Make Opal's spending the same.  LCM of 9 and 4 is 36.

Eva : Opal : Victoria
8 : 36 : 45

(b)

	Eva	Opal	Victoria
Before	8 u	36 u	45 u
Change		+ 9 u
After	8 u	45 u	45 u

Additional amount that Opal would have to spend to be the same as Victoria
= 45 u - 36 u
= 9 u

9 u = 315

1 u = 315 ÷ 9 = 35

Amount that Eva spent
= 8 u
= 8 x 35
= $280 

Answer(s): (a) 8 : 36 : 45; (b) $280