Three women, Irene, Tammy and Nora went on a shopping spree. 70% of Irene's spending was equal to ¹₅ of Tammy's spending. Nora's spending was  40% less than Tammy's. If Tammy spent $742 less, she would spend the same amount of money as Nora.

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

Irene	Tammy	Nora
2x5	7x5
	5x7	3x7
10 u	35 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Irene's spending is equal to ¹₅ of Tammy's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Irene's spending = 15 of Tammy's spending
710 of Irene's spending =1x75x7 of Tammy's spending
710 of Irene's spending = 735 of Tammy's spending

Irene : Tammy
10 : 35
2 : 7

Nora's spending in percent when compared to Tammy's
= 100% - 40%
= 60%

Tammy : Nora
100 : 60
5 : 3

Tammy's spending is the repeated identity.  Make Tammy's spending the same.  LCM of 7 and 5 is 35.

Irene : Tammy : Nora
10 : 35 : 21

(b)

	Irene	Tammy	Nora
Before	10 u	35 u	21 u
Change		- 14 u
After	10 u	21 u	21 u

Additional amount that Tammy would have to spend less to be the same as Nora
= 35 u - 21 u
= 14 u

14 u = 742

1 u = 742 ÷ 14 = 53

Amount that Nora spent
= 21 u
= 21 x 53
= $1113 

Answer(s): (a) 10 : 35 : 21; (b) $1113