Three women, Fiona, Gwen and Mary went on a shopping spree. 30% of Fiona's spending was equal to ¹₂ of Gwen's spending. Mary's spending was  60% less than Gwen's. If Gwen spent $1035 less, she would spend the same amount of money as Mary.

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

Fiona	Gwen	Mary
5x5	3x5
	5x3	2x3
25 u	15 u	6 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Fiona's spending is equal to ¹₂ of Gwen's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Fiona's spending = 12 of Gwen's spending
310 of Fiona's spending =1x32x3 of Gwen's spending
310 of Fiona's spending = 36 of Gwen's spending

Fiona : Gwen
10 : 6
5 : 3

Mary's spending in percent when compared to Gwen's
= 100% - 60%
= 40%

Gwen : Mary
100 : 40
5 : 2

Gwen's spending is the repeated identity.  Make Gwen's spending the same.  LCM of 3 and 5 is 15.

Fiona : Gwen : Mary
25 : 15 : 6

(b)

	Fiona	Gwen	Mary
Before	25 u	15 u	6 u
Change		- 9 u
After	25 u	6 u	6 u

Additional amount that Gwen would have to spend less to be the same as Mary
= 15 u - 6 u
= 9 u

9 u = 1035

1 u = 1035 ÷ 9 = 115

Amount that Mary spent
= 6 u
= 6 x 115
= $690 

Answer(s): (a) 25 : 15 : 6; (b) $690