Three women, Emily, Julie and Zoe went on a shopping spree. 30% of Emily's spending was equal to ¹₆ of Julie's spending. Zoe's spending was  40% more than Julie's. If Julie spent another $1494, she would spend the same amount of money as Zoe.

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

Emily	Julie	Zoe
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Emily's spending is equal to ¹₆ of Julie's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Emily's spending = 16 of Julie's spending
310 of Emily's spending =1x36x3 of Julie's spending
310 of Emily's spending = 318 of Julie's spending

Emily : Julie
10 : 18
5 : 9

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

Julie : Zoe
100 : 140
5 : 7

Julie's spending is the repeated identity.  Make Julie's spending the same.  LCM of 9 and 5 is 45.

Emily : Julie : Zoe
25 : 45 : 63

(b)

	Emily	Julie	Zoe
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

Additional amount that Julie would have to spend to be the same as Zoe
= 63 u - 45 u
= 18 u

18 u = 1494

1 u = 1494 ÷ 18 = 83

Amount that Emily spent
= 25 u
= 25 x 83
= $2075 

Answer(s): (a) 25 : 45 : 63; (b) $2075