Three women, Marion, Xuan and Penelope went on a shopping spree. 70% of Marion's spending was equal to ¹₆ of Xuan's spending. Penelope's spending was  80% less than Xuan's. If Xuan spent $8484 less, she would spend the same amount of money as Penelope.

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

Marion	Xuan	Penelope
5x5	21x5
	5x21	1x21
25 u	105 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Marion's spending is equal to ¹₆ of Xuan's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Marion's spending = 16 of Xuan's spending
710 of Marion's spending =1x76x7 of Xuan's spending
710 of Marion's spending = 742 of Xuan's spending

Marion : Xuan
10 : 42
5 : 21

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

Xuan : Penelope
100 : 20
5 : 1

Xuan's spending is the repeated identity.  Make Xuan's spending the same.  LCM of 21 and 5 is 105.

Marion : Xuan : Penelope
25 : 105 : 21

(b)

	Marion	Xuan	Penelope
Before	25 u	105 u	21 u
Change		- 84 u
After	25 u	21 u	21 u

Additional amount that Xuan would have to spend less to be the same as Penelope
= 105 u - 21 u
= 84 u

84 u = 8484

1 u = 8484 ÷ 84 = 101

Amount that Penelope spent
= 21 u
= 21 x 101
= $2121 

Answer(s): (a) 25 : 105 : 21; (b) $2121