Three women, Elyse, Olivia and Penelope went on a shopping spree. 70% of Elyse's spending was equal to ¹₅ of Olivia's spending. Penelope's spending was  60% less than Olivia's. If Olivia spent $1134 less, she would spend the same amount of money as Penelope.

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

Elyse	Olivia	Penelope
2x5	7x5
	5x7	2x7
10 u	35 u	14 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Elyse's spending is equal to ¹₅ of Olivia's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Elyse's spending = 15 of Olivia's spending
710 of Elyse's spending =1x75x7 of Olivia's spending
710 of Elyse's spending = 735 of Olivia's spending

Elyse : Olivia
10 : 35
2 : 7

Penelope's spending in percent when compared to Olivia's
= 100% - 60%
= 40%

Olivia : Penelope
100 : 40
5 : 2

Olivia's spending is the repeated identity.  Make Olivia's spending the same.  LCM of 7 and 5 is 35.

Elyse : Olivia : Penelope
10 : 35 : 14

(b)

	Elyse	Olivia	Penelope
Before	10 u	35 u	14 u
Change		- 21 u
After	10 u	14 u	14 u

Additional amount that Olivia would have to spend less to be the same as Penelope
= 35 u - 14 u
= 21 u

21 u = 1134

1 u = 1134 ÷ 21 = 54

Amount that Penelope spent
= 14 u
= 14 x 54
= $756 

Answer(s): (a) 10 : 35 : 14; (b) $756