Three women, Betty, Olivia and Lynn went on a shopping spree. 30% of Betty's spending was equal to ¹₅ of Olivia's spending. Lynn's spending was  25% less than Olivia's. If Olivia spent $303 less, she would spend the same amount of money as Lynn.

1. Find the ratio of Betty's spending to Olivia's to Lynn's.
2. How much did Lynn spend?

Betty	Olivia	Lynn
2x4	3x4
	4x3	3x3
8 u	12 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Betty's spending is equal to ¹₅ of Olivia's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Betty's spending = 15 of Olivia's spending
310 of Betty's spending =1x35x3 of Olivia's spending
310 of Betty's spending = 315 of Olivia's spending

Betty : Olivia
10 : 15
2 : 3

Lynn's spending in percent when compared to Olivia's
= 100% - 25%
= 75%

Olivia : Lynn
100 : 75
4 : 3

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

Betty : Olivia : Lynn
8 : 12 : 9

(b)

	Betty	Olivia	Lynn
Before	8 u	12 u	9 u
Change		- 3 u
After	8 u	9 u	9 u

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

3 u = 303

1 u = 303 ÷ 3 = 101

Amount that Lynn spent
= 9 u
= 9 x 101
= $909 

Answer(s): (a) 8 : 12 : 9; (b) $909