Three women, Fanny, Tammy and Jane went on a shopping spree. 70% of Fanny's spending was equal to ¹₅ of Tammy's spending. Jane's spending was  80% less than Tammy's. If Tammy spent $1036 less, she would spend the same amount of money as Jane.

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

Fanny	Tammy	Jane
2x5	7x5
	5x7	1x7
10 u	35 u	7 u

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

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

Fanny : Tammy
10 : 35
2 : 7

Jane's spending in percent when compared to Tammy's
= 100% - 80%
= 20%

Tammy : Jane
100 : 20
5 : 1

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

Fanny : Tammy : Jane
10 : 35 : 7

(b)

	Fanny	Tammy	Jane
Before	10 u	35 u	7 u
Change		- 28 u
After	10 u	7 u	7 u

Additional amount that Tammy would have to spend less to be the same as Jane
= 35 u - 7 u
= 28 u

28 u = 1036

1 u = 1036 ÷ 28 = 37

Amount that Jane spent
= 7 u
= 7 x 37
= $259 

Answer(s): (a) 10 : 35 : 7; (b) $259