Three women, Xuan, Tammy and Eva went on a shopping spree. 70% of Xuan's spending was equal to ¹₆ of Tammy's spending. Eva's spending was  25% more than Tammy's. If Tammy spent another $1449, she would spend the same amount of money as Eva.

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

Xuan	Tammy	Eva
5x4	21x4
	4x21	5x21
20 u	84 u	105 u

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

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

Xuan : Tammy
10 : 42
5 : 21

Eva's spending in percent when compared to Tammy's
= 100% + 25%
= 125%

Tammy : Eva
100 : 125
4 : 5

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

Xuan : Tammy : Eva
20 : 84 : 105

(b)

	Xuan	Tammy	Eva
Before	20 u	84 u	105 u
Change		+ 21 u
After	20 u	105 u	105 u

Additional amount that Tammy would have to spend to be the same as Eva
= 105 u - 84 u
= 21 u

21 u = 1449

1 u = 1449 ÷ 21 = 69

Amount that Xuan spent
= 20 u
= 20 x 69
= $1380 

Answer(s): (a) 20 : 84 : 105; (b) $1380