Three women, Gabby, Anna and Lynn went on a shopping spree. 30% of Gabby's spending was equal to ¹₅ of Anna's spending. Lynn's spending was  60% less than Anna's. If Anna spent $378 less, she would spend the same amount of money as Lynn.

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

Gabby	Anna	Lynn
2x5	3x5
	5x3	2x3
10 u	15 u	6 u

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

310 of Gabby's spending = 15 of Anna's spending
310 of Gabby's spending =1x35x3 of Anna's spending
310 of Gabby's spending = 315 of Anna's spending

Gabby : Anna
10 : 15
2 : 3

Lynn's spending in percent when compared to Anna's
= 100% - 60%
= 40%

Anna : Lynn
100 : 40
5 : 2

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

Gabby : Anna : Lynn
10 : 15 : 6

(b)

	Gabby	Anna	Lynn
Before	10 u	15 u	6 u
Change		- 9 u
After	10 u	6 u	6 u

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

9 u = 378

1 u = 378 ÷ 9 = 42

Amount that Lynn spent
= 6 u
= 6 x 42
= $252 

Answer(s): (a) 10 : 15 : 6; (b) $252