Three women, Esther, Barbara and Lynn went on a shopping spree. 70% of Esther's spending was equal to ¹₆ of Barbara's spending. Lynn's spending was  25% less than Barbara's. If Barbara spent $819 less, she would spend the same amount of money as Lynn.

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

Esther	Barbara	Lynn
5x4	21x4
	4x21	3x21
20 u	84 u	63 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Esther's spending is equal to ¹₆ of Barbara's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Esther's spending = 16 of Barbara's spending
710 of Esther's spending =1x76x7 of Barbara's spending
710 of Esther's spending = 742 of Barbara's spending

Esther : Barbara
10 : 42
5 : 21

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

Barbara : Lynn
100 : 75
4 : 3

Barbara's spending is the repeated identity.  Make Barbara's spending the same.  LCM of 21 and 4 is 84.

Esther : Barbara : Lynn
20 : 84 : 63

(b)

	Esther	Barbara	Lynn
Before	20 u	84 u	63 u
Change		- 21 u
After	20 u	63 u	63 u

Additional amount that Barbara would have to spend less to be the same as Lynn
= 84 u - 63 u
= 21 u

21 u = 819

1 u = 819 ÷ 21 = 39

Amount that Lynn spent
= 63 u
= 63 x 39
= $2457 

Answer(s): (a) 20 : 84 : 63; (b) $2457