Three women, Mary, Diana and Opal went on a shopping spree. 30% of Mary's spending was equal to ¹₂ of Diana's spending. Opal's spending was  25% less than Diana's. If Diana spent $309 less, she would spend the same amount of money as Opal.

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

Mary	Diana	Opal
5x4	3x4
	4x3	3x3
20 u	12 u	9 u

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

310 of Mary's spending = 12 of Diana's spending
310 of Mary's spending =1x32x3 of Diana's spending
310 of Mary's spending = 36 of Diana's spending

Mary : Diana
10 : 6
5 : 3

Opal's spending in percent when compared to Diana's
= 100% - 25%
= 75%

Diana : Opal
100 : 75
4 : 3

Diana's spending is the repeated identity.  Make Diana's spending the same.  LCM of 3 and 4 is 12.

Mary : Diana : Opal
20 : 12 : 9

(b)

	Mary	Diana	Opal
Before	20 u	12 u	9 u
Change		- 3 u
After	20 u	9 u	9 u

Additional amount that Diana would have to spend less to be the same as Opal
= 12 u - 9 u
= 3 u

3 u = 309

1 u = 309 ÷ 3 = 103

Amount that Opal spent
= 9 u
= 9 x 103
= $927 

Answer(s): (a) 20 : 12 : 9; (b) $927