Three women, Marion, Joelle and Xylia went on a shopping spree. 70% of Marion's spending was equal to ¹₆ of Joelle's spending. Xylia's spending was  50% more than Joelle's. If Joelle spent another $1029, she would spend the same amount of money as Xylia.

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

Marion	Joelle	Xylia
5x2	21x2
	2x21	3x21
10 u	42 u	63 u

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

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

Marion : Joelle
10 : 42
5 : 21

Xylia's spending in percent when compared to Joelle's
= 100% + 50%
= 150%

Joelle : Xylia
100 : 150
2 : 3

Joelle's spending is the repeated identity.  Make Joelle's spending the same.  LCM of 21 and 2 is 42.

Marion : Joelle : Xylia
10 : 42 : 63

(b)

	Marion	Joelle	Xylia
Before	10 u	42 u	63 u
Change		+ 21 u
After	10 u	63 u	63 u

Additional amount that Joelle would have to spend to be the same as Xylia
= 63 u - 42 u
= 21 u

21 u = 1029

1 u = 1029 ÷ 21 = 49

Amount that Marion spent
= 10 u
= 10 x 49
= $490 

Answer(s): (a) 10 : 42 : 63; (b) $490