Three women, Fanny, Tammy and Shannon went on a shopping spree. 70% of Fanny's spending was equal to ¹₆ of Tammy's spending. Shannon's spending was  40% less than Tammy's. If Tammy spent $4536 less, she would spend the same amount of money as Shannon.

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

Fanny	Tammy	Shannon
5x5	21x5
	5x21	3x21
25 u	105 u	63 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Fanny's spending is equal to ¹₆ of Tammy's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Fanny's spending = 16 of Tammy's spending
710 of Fanny's spending =1x76x7 of Tammy's spending
710 of Fanny's spending = 742 of Tammy's spending

Fanny : Tammy
10 : 42
5 : 21

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

Tammy : Shannon
100 : 60
5 : 3

Tammy's spending is the repeated identity.  Make Tammy's spending the same.  LCM of 21 and 5 is 105.

Fanny : Tammy : Shannon
25 : 105 : 63

(b)

	Fanny	Tammy	Shannon
Before	25 u	105 u	63 u
Change		- 42 u
After	25 u	63 u	63 u

Additional amount that Tammy would have to spend less to be the same as Shannon
= 105 u - 63 u
= 42 u

42 u = 4536

1 u = 4536 ÷ 42 = 108

Amount that Shannon spent
= 63 u
= 63 x 108
= $6804 

Answer(s): (a) 25 : 105 : 63; (b) $6804