Three women, Diana, Emma and Gillian went on a shopping spree. 90% of Diana's spending was equal to ¹₆ of Emma's spending. Gillian's spending was  80% less than Emma's. If Emma spent $9072 less, she would spend the same amount of money as Gillian.

1. Find the ratio of Diana's spending to Emma's to Gillian's.
2. How much did Gillian spend?

Diana	Emma	Gillian
5x5	27x5
	5x27	1x27
25 u	135 u	27 u

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

910 of Diana's spending = 16 of Emma's spending
910 of Diana's spending =1x96x9 of Emma's spending
910 of Diana's spending = 954 of Emma's spending

Diana : Emma
10 : 54
5 : 27

Gillian's spending in percent when compared to Emma's
= 100% - 80%
= 20%

Emma : Gillian
100 : 20
5 : 1

Emma's spending is the repeated identity.  Make Emma's spending the same.  LCM of 27 and 5 is 135.

Diana : Emma : Gillian
25 : 135 : 27

(b)

	Diana	Emma	Gillian
Before	25 u	135 u	27 u
Change		- 108 u
After	25 u	27 u	27 u

Additional amount that Emma would have to spend less to be the same as Gillian
= 135 u - 27 u
= 108 u

108 u = 9072

1 u = 9072 ÷ 108 = 84

Amount that Gillian spent
= 27 u
= 27 x 84
= $2268 

Answer(s): (a) 25 : 135 : 27; (b) $2268