Three women, Elyse, Olivia and Victoria went on a shopping spree. 90% of Elyse's spending was equal to ¹₂ of Olivia's spending. Victoria's spending was  60% more than Olivia's. If Olivia spent another $1377, she would spend the same amount of money as Victoria.

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

Elyse	Olivia	Victoria
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Elyse's spending is equal to ¹₂ of Olivia's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Elyse's spending = 12 of Olivia's spending
910 of Elyse's spending =1x92x9 of Olivia's spending
910 of Elyse's spending = 918 of Olivia's spending

Elyse : Olivia
10 : 18
5 : 9

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

Olivia : Victoria
100 : 160
5 : 8

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

Elyse : Olivia : Victoria
25 : 45 : 72

(b)

	Elyse	Olivia	Victoria
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

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

27 u = 1377

1 u = 1377 ÷ 27 = 51

Amount that Elyse spent
= 25 u
= 25 x 51
= $1275 

Answer(s): (a) 25 : 45 : 72; (b) $1275