Three women, Joelle, Yoko and Yen went on a shopping spree. 90% of Joelle's spending was equal to ¹₂ of Yoko's spending. Yen's spending was  25% less than Yoko's. If Yoko spent $792 less, she would spend the same amount of money as Yen.

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

Joelle	Yoko	Yen
5x4	9x4
	4x9	3x9
20 u	36 u	27 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Joelle's spending is equal to ¹₂ of Yoko's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Joelle's spending = 12 of Yoko's spending
910 of Joelle's spending =1x92x9 of Yoko's spending
910 of Joelle's spending = 918 of Yoko's spending

Joelle : Yoko
10 : 18
5 : 9

Yen's spending in percent when compared to Yoko's
= 100% - 25%
= 75%

Yoko : Yen
100 : 75
4 : 3

Yoko's spending is the repeated identity.  Make Yoko's spending the same.  LCM of 9 and 4 is 36.

Joelle : Yoko : Yen
20 : 36 : 27

(b)

	Joelle	Yoko	Yen
Before	20 u	36 u	27 u
Change		- 9 u
After	20 u	27 u	27 u

Additional amount that Yoko would have to spend less to be the same as Yen
= 36 u - 27 u
= 9 u

9 u = 792

1 u = 792 ÷ 9 = 88

Amount that Yen spent
= 27 u
= 27 x 88
= $2376 

Answer(s): (a) 20 : 36 : 27; (b) $2376