Three women, Anna, Shannon and Dana went on a shopping spree. 70% of Anna's spending was equal to ¹₆ of Shannon's spending. Dana's spending was  25% less than Shannon's. If Shannon spent $714 less, she would spend the same amount of money as Dana.

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

Anna	Shannon	Dana
5x4	21x4
	4x21	3x21
20 u	84 u	63 u

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

710 of Anna's spending = 16 of Shannon's spending
710 of Anna's spending =1x76x7 of Shannon's spending
710 of Anna's spending = 742 of Shannon's spending

Anna : Shannon
10 : 42
5 : 21

Dana's spending in percent when compared to Shannon's
= 100% - 25%
= 75%

Shannon : Dana
100 : 75
4 : 3

Shannon's spending is the repeated identity.  Make Shannon's spending the same.  LCM of 21 and 4 is 84.

Anna : Shannon : Dana
20 : 84 : 63

(b)

	Anna	Shannon	Dana
Before	20 u	84 u	63 u
Change		- 21 u
After	20 u	63 u	63 u

Additional amount that Shannon would have to spend less to be the same as Dana
= 84 u - 63 u
= 21 u

21 u = 714

1 u = 714 ÷ 21 = 34

Amount that Dana spent
= 63 u
= 63 x 34
= $2142 

Answer(s): (a) 20 : 84 : 63; (b) $2142