Three women, Tammy, Gabby and Nora went on a shopping spree. 70% of Tammy's spending was equal to ¹₂ of Gabby's spending. Nora's spending was  70% less than Gabby's. If Gabby spent $1372 less, she would spend the same amount of money as Nora.

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

Tammy	Gabby	Nora
5x10	7x10
	10x7	3x7
50 u	70 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Tammy's spending is equal to ¹₂ of Gabby's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Tammy's spending = 12 of Gabby's spending
710 of Tammy's spending =1x72x7 of Gabby's spending
710 of Tammy's spending = 714 of Gabby's spending

Tammy : Gabby
10 : 14
5 : 7

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

Gabby : Nora
100 : 30
10 : 3

Gabby's spending is the repeated identity.  Make Gabby's spending the same.  LCM of 7 and 10 is 70.

Tammy : Gabby : Nora
50 : 70 : 21

(b)

	Tammy	Gabby	Nora
Before	50 u	70 u	21 u
Change		- 49 u
After	50 u	21 u	21 u

Additional amount that Gabby would have to spend less to be the same as Nora
= 70 u - 21 u
= 49 u

49 u = 1372

1 u = 1372 ÷ 49 = 28

Amount that Nora spent
= 21 u
= 21 x 28
= $588 

Answer(s): (a) 50 : 70 : 21; (b) $588