Three women, Jen, Eva and Min went on a shopping spree. 70% of Jen's spending was equal to ¹₂ of Eva's spending. Min's spending was  70% less than Eva's. If Eva spent $2254 less, she would spend the same amount of money as Min.

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

Jen	Eva	Min
5x10	7x10
	10x7	3x7
50 u	70 u	21 u

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

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

Jen : Eva
10 : 14
5 : 7

Min's spending in percent when compared to Eva's
= 100% - 70%
= 30%

Eva : Min
100 : 30
10 : 3

Eva's spending is the repeated identity.  Make Eva's spending the same.  LCM of 7 and 10 is 70.

Jen : Eva : Min
50 : 70 : 21

(b)

	Jen	Eva	Min
Before	50 u	70 u	21 u
Change		- 49 u
After	50 u	21 u	21 u

Additional amount that Eva would have to spend less to be the same as Min
= 70 u - 21 u
= 49 u

49 u = 2254

1 u = 2254 ÷ 49 = 46

Amount that Min spent
= 21 u
= 21 x 46
= $966 

Answer(s): (a) 50 : 70 : 21; (b) $966