Three women, Dana, Fanny and Fiona went on a shopping spree. 70% of Dana's spending was equal to ¹₆ of Fanny's spending. Fiona's spending was  50% more than Fanny's. If Fanny spent another $798, she would spend the same amount of money as Fiona.

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

Dana	Fanny	Fiona
5x2	21x2
	2x21	3x21
10 u	42 u	63 u

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

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

Dana : Fanny
10 : 42
5 : 21

Fiona's spending in percent when compared to Fanny's
= 100% + 50%
= 150%

Fanny : Fiona
100 : 150
2 : 3

Fanny's spending is the repeated identity.  Make Fanny's spending the same.  LCM of 21 and 2 is 42.

Dana : Fanny : Fiona
10 : 42 : 63

(b)

	Dana	Fanny	Fiona
Before	10 u	42 u	63 u
Change		+ 21 u
After	10 u	63 u	63 u

Additional amount that Fanny would have to spend to be the same as Fiona
= 63 u - 42 u
= 21 u

21 u = 798

1 u = 798 ÷ 21 = 38

Amount that Dana spent
= 10 u
= 10 x 38
= $380 

Answer(s): (a) 10 : 42 : 63; (b) $380