Three women, Tammy, Zoe and Yoko went on a shopping spree. 30% of Tammy's spending was equal to ¹₅ of Zoe's spending. Yoko's spending was  40% more than Zoe's. If Zoe spent another $384, she would spend the same amount of money as Yoko.

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

Tammy	Zoe	Yoko
2x5	3x5
	5x3	7x3
10 u	15 u	21 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Tammy's spending is equal to ¹₅ of Zoe's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Tammy's spending = 15 of Zoe's spending
310 of Tammy's spending =1x35x3 of Zoe's spending
310 of Tammy's spending = 315 of Zoe's spending

Tammy : Zoe
10 : 15
2 : 3

Yoko's spending in percent when compared to Zoe's
= 100% + 40%
= 140%

Zoe : Yoko
100 : 140
5 : 7

Zoe's spending is the repeated identity.  Make Zoe's spending the same.  LCM of 3 and 5 is 15.

Tammy : Zoe : Yoko
10 : 15 : 21

(b)

	Tammy	Zoe	Yoko
Before	10 u	15 u	21 u
Change		+ 6 u
After	10 u	21 u	21 u

Additional amount that Zoe would have to spend to be the same as Yoko
= 21 u - 15 u
= 6 u

6 u = 384

1 u = 384 ÷ 6 = 64

Amount that Tammy spent
= 10 u
= 10 x 64
= $640 

Answer(s): (a) 10 : 15 : 21; (b) $640