Three women, Fanny, Min and Gwen went on a shopping spree. 90% of Fanny's spending was equal to ¹₅ of Min's spending. Gwen's spending was  70% less than Min's. If Min spent $1512 less, she would spend the same amount of money as Gwen.

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

Fanny	Min	Gwen
2x10	9x10
	10x9	3x9
20 u	90 u	27 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Fanny's spending is equal to ¹₅ of Min's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Fanny's spending = 15 of Min's spending
910 of Fanny's spending =1x95x9 of Min's spending
910 of Fanny's spending = 945 of Min's spending

Fanny : Min
10 : 45
2 : 9

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

Min : Gwen
100 : 30
10 : 3

Min's spending is the repeated identity.  Make Min's spending the same.  LCM of 9 and 10 is 90.

Fanny : Min : Gwen
20 : 90 : 27

(b)

	Fanny	Min	Gwen
Before	20 u	90 u	27 u
Change		- 63 u
After	20 u	27 u	27 u

Additional amount that Min would have to spend less to be the same as Gwen
= 90 u - 27 u
= 63 u

63 u = 1512

1 u = 1512 ÷ 63 = 24

Amount that Gwen spent
= 27 u
= 27 x 24
= $648 

Answer(s): (a) 20 : 90 : 27; (b) $648