Three women, Betty, Gwen and Eva went on a shopping spree. 70% of Betty's spending was equal to ¹₅ of Gwen's spending. Eva's spending was  40% more than Gwen's. If Gwen spent another $1316, she would spend the same amount of money as Eva.

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

Betty	Gwen	Eva
2x5	7x5
	5x7	7x7
10 u	35 u	49 u

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

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

Betty : Gwen
10 : 35
2 : 7

Eva's spending in percent when compared to Gwen's
= 100% + 40%
= 140%

Gwen : Eva
100 : 140
5 : 7

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

Betty : Gwen : Eva
10 : 35 : 49

(b)

	Betty	Gwen	Eva
Before	10 u	35 u	49 u
Change		+ 14 u
After	10 u	49 u	49 u

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

14 u = 1316

1 u = 1316 ÷ 14 = 94

Amount that Betty spent
= 10 u
= 10 x 94
= $940 

Answer(s): (a) 10 : 35 : 49; (b) $940