Three women, Eva, Olivia and Gillian went on a shopping spree. 90% of Eva's spending was equal to ¹₆ of Olivia's spending. Gillian's spending was  50% more than Olivia's. If Olivia spent another $1944, she would spend the same amount of money as Gillian.

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

Eva	Olivia	Gillian
5x2	27x2
	2x27	3x27
10 u	54 u	81 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Eva's spending is equal to ¹₆ of Olivia's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Eva's spending = 16 of Olivia's spending
910 of Eva's spending =1x96x9 of Olivia's spending
910 of Eva's spending = 954 of Olivia's spending

Eva : Olivia
10 : 54
5 : 27

Gillian's spending in percent when compared to Olivia's
= 100% + 50%
= 150%

Olivia : Gillian
100 : 150
2 : 3

Olivia's spending is the repeated identity.  Make Olivia's spending the same.  LCM of 27 and 2 is 54.

Eva : Olivia : Gillian
10 : 54 : 81

(b)

	Eva	Olivia	Gillian
Before	10 u	54 u	81 u
Change		+ 27 u
After	10 u	81 u	81 u

Additional amount that Olivia would have to spend to be the same as Gillian
= 81 u - 54 u
= 27 u

27 u = 1944

1 u = 1944 ÷ 27 = 72

Amount that Eva spent
= 10 u
= 10 x 72
= $720 

Answer(s): (a) 10 : 54 : 81; (b) $720