Three women, Dana, Yen and Victoria went on a shopping spree. 70% of Dana's spending was equal to ¹₆ of Yen's spending. Victoria's spending was  60% less than Yen's. If Yen spent $5040 less, she would spend the same amount of money as Victoria.

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

Dana	Yen	Victoria
5x5	21x5
	5x21	2x21
25 u	105 u	42 u

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

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

Dana : Yen
10 : 42
5 : 21

Victoria's spending in percent when compared to Yen's
= 100% - 60%
= 40%

Yen : Victoria
100 : 40
5 : 2

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

Dana : Yen : Victoria
25 : 105 : 42

(b)

	Dana	Yen	Victoria
Before	25 u	105 u	42 u
Change		- 63 u
After	25 u	42 u	42 u

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

63 u = 5040

1 u = 5040 ÷ 63 = 80

Amount that Victoria spent
= 42 u
= 42 x 80
= $3360 

Answer(s): (a) 25 : 105 : 42; (b) $3360