Three women, Dana, Jade and Tiffany went on a shopping spree. 30% of Dana's spending was equal to ¹₂ of Jade's spending. Tiffany's spending was  60% more than Jade's. If Jade spent another $513, she would spend the same amount of money as Tiffany.

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

Dana	Jade	Tiffany
5x5	3x5
	5x3	8x3
25 u	15 u	24 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Dana's spending is equal to ¹₂ of Jade's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Dana's spending = 12 of Jade's spending
310 of Dana's spending =1x32x3 of Jade's spending
310 of Dana's spending = 36 of Jade's spending

Dana : Jade
10 : 6
5 : 3

Tiffany's spending in percent when compared to Jade's
= 100% + 60%
= 160%

Jade : Tiffany
100 : 160
5 : 8

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

Dana : Jade : Tiffany
25 : 15 : 24

(b)

	Dana	Jade	Tiffany
Before	25 u	15 u	24 u
Change		+ 9 u
After	25 u	24 u	24 u

Additional amount that Jade would have to spend to be the same as Tiffany
= 24 u - 15 u
= 9 u

9 u = 513

1 u = 513 ÷ 9 = 57

Amount that Dana spent
= 25 u
= 25 x 57
= $1425 

Answer(s): (a) 25 : 15 : 24; (b) $1425