Three women, Yoko, Joelle and Fanny went on a shopping spree. 30% of Yoko's spending was equal to ¹₆ of Joelle's spending. Fanny's spending was  50% more than Joelle's. If Joelle spent another $180, she would spend the same amount of money as Fanny.

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

Yoko	Joelle	Fanny
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Yoko's spending is equal to ¹₆ of Joelle's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Yoko's spending = 16 of Joelle's spending
310 of Yoko's spending =1x36x3 of Joelle's spending
310 of Yoko's spending = 318 of Joelle's spending

Yoko : Joelle
10 : 18
5 : 9

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

Joelle : Fanny
100 : 150
2 : 3

Joelle's spending is the repeated identity.  Make Joelle's spending the same.  LCM of 9 and 2 is 18.

Yoko : Joelle : Fanny
10 : 18 : 27

(b)

	Yoko	Joelle	Fanny
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

Additional amount that Joelle would have to spend to be the same as Fanny
= 27 u - 18 u
= 9 u

9 u = 180

1 u = 180 ÷ 9 = 20

Amount that Yoko spent
= 10 u
= 10 x 20
= $200 

Answer(s): (a) 10 : 18 : 27; (b) $200