Three women, Jean, Tammy and Natalie went on a shopping spree. 70% of Jean's spending was equal to ¹₂ of Tammy's spending. Natalie's spending was  40% less than Tammy's. If Tammy spent $462 less, she would spend the same amount of money as Natalie.

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

Jean	Tammy	Natalie
5x5	7x5
	5x7	3x7
25 u	35 u	21 u

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

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

Jean : Tammy
10 : 14
5 : 7

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

Tammy : Natalie
100 : 60
5 : 3

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

Jean : Tammy : Natalie
25 : 35 : 21

(b)

	Jean	Tammy	Natalie
Before	25 u	35 u	21 u
Change		- 14 u
After	25 u	21 u	21 u

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

14 u = 462

1 u = 462 ÷ 14 = 33

Amount that Natalie spent
= 21 u
= 21 x 33
= $693 

Answer(s): (a) 25 : 35 : 21; (b) $693