Three women, Winnie, Marion and Erika went on a shopping spree. 90% of Winnie's spending was equal to ¹₅ of Marion's spending. Erika's spending was  40% less than Marion's. If Marion spent $1008 less, she would spend the same amount of money as Erika.

1. Find the ratio of Winnie's spending to Marion's to Erika's.
2. How much did Erika spend?

Winnie	Marion	Erika
2x5	9x5
	5x9	3x9
10 u	45 u	27 u

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

910 of Winnie's spending = 15 of Marion's spending
910 of Winnie's spending =1x95x9 of Marion's spending
910 of Winnie's spending = 945 of Marion's spending

Winnie : Marion
10 : 45
2 : 9

Erika's spending in percent when compared to Marion's
= 100% - 40%
= 60%

Marion : Erika
100 : 60
5 : 3

Marion's spending is the repeated identity.  Make Marion's spending the same.  LCM of 9 and 5 is 45.

Winnie : Marion : Erika
10 : 45 : 27

(b)

	Winnie	Marion	Erika
Before	10 u	45 u	27 u
Change		- 18 u
After	10 u	27 u	27 u

Additional amount that Marion would have to spend less to be the same as Erika
= 45 u - 27 u
= 18 u

18 u = 1008

1 u = 1008 ÷ 18 = 56

Amount that Erika spent
= 27 u
= 27 x 56
= $1512 

Answer(s): (a) 10 : 45 : 27; (b) $1512