Three women, Yoko, Ivory and Penelope went on a shopping spree. 70% of Yoko's spending was equal to ¹₂ of Ivory's spending. Penelope's spending was  80% less than Ivory's. If Ivory spent $1148 less, she would spend the same amount of money as Penelope.

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

Yoko	Ivory	Penelope
5x5	7x5
	5x7	1x7
25 u	35 u	7 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Yoko's spending is equal to ¹₂ of Ivory's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Yoko's spending = 12 of Ivory's spending
710 of Yoko's spending =1x72x7 of Ivory's spending
710 of Yoko's spending = 714 of Ivory's spending

Yoko : Ivory
10 : 14
5 : 7

Penelope's spending in percent when compared to Ivory's
= 100% - 80%
= 20%

Ivory : Penelope
100 : 20
5 : 1

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

Yoko : Ivory : Penelope
25 : 35 : 7

(b)

	Yoko	Ivory	Penelope
Before	25 u	35 u	7 u
Change		- 28 u
After	25 u	7 u	7 u

Additional amount that Ivory would have to spend less to be the same as Penelope
= 35 u - 7 u
= 28 u

28 u = 1148

1 u = 1148 ÷ 28 = 41

Amount that Penelope spent
= 7 u
= 7 x 41
= $287 

Answer(s): (a) 25 : 35 : 7; (b) $287