Three women, Jen, Yoko and Zara went on a shopping spree. 70% of Jen's spending was equal to ¹₂ of Yoko's spending. Zara's spending was  40% more than Yoko's. If Yoko spent another $1204, she would spend the same amount of money as Zara.

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

Jen	Yoko	Zara
5x5	7x5
	5x7	7x7
25 u	35 u	49 u

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

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

Jen : Yoko
10 : 14
5 : 7

Zara's spending in percent when compared to Yoko's
= 100% + 40%
= 140%

Yoko : Zara
100 : 140
5 : 7

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

Jen : Yoko : Zara
25 : 35 : 49

(b)

	Jen	Yoko	Zara
Before	25 u	35 u	49 u
Change		+ 14 u
After	25 u	49 u	49 u

Additional amount that Yoko would have to spend to be the same as Zara
= 49 u - 35 u
= 14 u

14 u = 1204

1 u = 1204 ÷ 14 = 86

Amount that Jen spent
= 25 u
= 25 x 86
= $2150 

Answer(s): (a) 25 : 35 : 49; (b) $2150