Three women, Eva, Betty and Gem went on a shopping spree. 70% of Eva's spending was equal to ¹₅ of Betty's spending. Gem's spending was  40% less than Betty's. If Betty spent $630 less, she would spend the same amount of money as Gem.

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

Eva	Betty	Gem
2x5	7x5
	5x7	3x7
10 u	35 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Eva's spending is equal to ¹₅ of Betty's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Eva's spending = 15 of Betty's spending
710 of Eva's spending =1x75x7 of Betty's spending
710 of Eva's spending = 735 of Betty's spending

Eva : Betty
10 : 35
2 : 7

Gem's spending in percent when compared to Betty's
= 100% - 40%
= 60%

Betty : Gem
100 : 60
5 : 3

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

Eva : Betty : Gem
10 : 35 : 21

(b)

	Eva	Betty	Gem
Before	10 u	35 u	21 u
Change		- 14 u
After	10 u	21 u	21 u

Additional amount that Betty would have to spend less to be the same as Gem
= 35 u - 21 u
= 14 u

14 u = 630

1 u = 630 ÷ 14 = 45

Amount that Gem spent
= 21 u
= 21 x 45
= $945 

Answer(s): (a) 10 : 35 : 21; (b) $945