Three women, Jaslyn, Gabby and Linda went on a shopping spree. 90% of Jaslyn's spending was equal to ¹₆ of Gabby's spending. Linda's spending was  70% less than Gabby's. If Gabby spent $5103 less, she would spend the same amount of money as Linda.

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

Jaslyn	Gabby	Linda
5x10	27x10
	10x27	3x27
50 u	270 u	81 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Jaslyn's spending is equal to ¹₆ of Gabby's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Jaslyn's spending = 16 of Gabby's spending
910 of Jaslyn's spending =1x96x9 of Gabby's spending
910 of Jaslyn's spending = 954 of Gabby's spending

Jaslyn : Gabby
10 : 54
5 : 27

Linda's spending in percent when compared to Gabby's
= 100% - 70%
= 30%

Gabby : Linda
100 : 30
10 : 3

Gabby's spending is the repeated identity.  Make Gabby's spending the same.  LCM of 27 and 10 is 270.

Jaslyn : Gabby : Linda
50 : 270 : 81

(b)

	Jaslyn	Gabby	Linda
Before	50 u	270 u	81 u
Change		- 189 u
After	50 u	81 u	81 u

Additional amount that Gabby would have to spend less to be the same as Linda
= 270 u - 81 u
= 189 u

189 u = 5103

1 u = 5103 ÷ 189 = 27

Amount that Linda spent
= 81 u
= 81 x 27
= $2187 

Answer(s): (a) 50 : 270 : 81; (b) $2187