Three women, Barbara, Gabby and Usha went on a shopping spree. 70% of Barbara's spending was equal to ¹₆ of Gabby's spending. Usha's spending was  80% less than Gabby's. If Gabby spent $4620 less, she would spend the same amount of money as Usha.

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

Barbara	Gabby	Usha
5x5	21x5
	5x21	1x21
25 u	105 u	21 u

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

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

Barbara : Gabby
10 : 42
5 : 21

Usha's spending in percent when compared to Gabby's
= 100% - 80%
= 20%

Gabby : Usha
100 : 20
5 : 1

Gabby's spending is the repeated identity.  Make Gabby's spending the same.  LCM of 21 and 5 is 105.

Barbara : Gabby : Usha
25 : 105 : 21

(b)

	Barbara	Gabby	Usha
Before	25 u	105 u	21 u
Change		- 84 u
After	25 u	21 u	21 u

Additional amount that Gabby would have to spend less to be the same as Usha
= 105 u - 21 u
= 84 u

84 u = 4620

1 u = 4620 ÷ 84 = 55

Amount that Usha spent
= 21 u
= 21 x 55
= $1155 

Answer(s): (a) 25 : 105 : 21; (b) $1155