Three women, Fiona, Wendy and Dana went on a shopping spree. 70% of Fiona's spending was equal to ¹₂ of Wendy's spending. Dana's spending was  80% less than Wendy's. If Wendy spent $1372 less, she would spend the same amount of money as Dana.

1. Find the ratio of Fiona's spending to Wendy's to Dana's.
2. How much did Dana spend?

Fiona	Wendy	Dana
5x5	7x5
	5x7	1x7
25 u	35 u	7 u

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

710 of Fiona's spending = 12 of Wendy's spending
710 of Fiona's spending =1x72x7 of Wendy's spending
710 of Fiona's spending = 714 of Wendy's spending

Fiona : Wendy
10 : 14
5 : 7

Dana's spending in percent when compared to Wendy's
= 100% - 80%
= 20%

Wendy : Dana
100 : 20
5 : 1

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

Fiona : Wendy : Dana
25 : 35 : 7

(b)

	Fiona	Wendy	Dana
Before	25 u	35 u	7 u
Change		- 28 u
After	25 u	7 u	7 u

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

28 u = 1372

1 u = 1372 ÷ 28 = 49

Amount that Dana spent
= 7 u
= 7 x 49
= $343 

Answer(s): (a) 25 : 35 : 7; (b) $343