Three women, Wendy, Gillian and Opal went on a shopping spree. 30% of Wendy's spending was equal to ¹₂ of Gillian's spending. Opal's spending was  60% less than Gillian's. If Gillian spent $1026 less, she would spend the same amount of money as Opal.

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

Wendy	Gillian	Opal
5x5	3x5
	5x3	2x3
25 u	15 u	6 u

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

310 of Wendy's spending = 12 of Gillian's spending
310 of Wendy's spending =1x32x3 of Gillian's spending
310 of Wendy's spending = 36 of Gillian's spending

Wendy : Gillian
10 : 6
5 : 3

Opal's spending in percent when compared to Gillian's
= 100% - 60%
= 40%

Gillian : Opal
100 : 40
5 : 2

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

Wendy : Gillian : Opal
25 : 15 : 6

(b)

	Wendy	Gillian	Opal
Before	25 u	15 u	6 u
Change		- 9 u
After	25 u	6 u	6 u

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

9 u = 1026

1 u = 1026 ÷ 9 = 114

Amount that Opal spent
= 6 u
= 6 x 114
= $684 

Answer(s): (a) 25 : 15 : 6; (b) $684