Three women, Marion, Dana and Gwen went on a shopping spree. 90% of Marion's spending was equal to ¹₆ of Dana's spending. Gwen's spending was  25% less than Dana's. If Dana spent $1836 less, she would spend the same amount of money as Gwen.

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

Marion	Dana	Gwen
5x4	27x4
	4x27	3x27
20 u	108 u	81 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Marion's spending is equal to ¹₆ of Dana's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Marion's spending = 16 of Dana's spending
910 of Marion's spending =1x96x9 of Dana's spending
910 of Marion's spending = 954 of Dana's spending

Marion : Dana
10 : 54
5 : 27

Gwen's spending in percent when compared to Dana's
= 100% - 25%
= 75%

Dana : Gwen
100 : 75
4 : 3

Dana's spending is the repeated identity.  Make Dana's spending the same.  LCM of 27 and 4 is 108.

Marion : Dana : Gwen
20 : 108 : 81

(b)

	Marion	Dana	Gwen
Before	20 u	108 u	81 u
Change		- 27 u
After	20 u	81 u	81 u

Additional amount that Dana would have to spend less to be the same as Gwen
= 108 u - 81 u
= 27 u

27 u = 1836

1 u = 1836 ÷ 27 = 68

Amount that Gwen spent
= 81 u
= 81 x 68
= $5508 

Answer(s): (a) 20 : 108 : 81; (b) $5508