Three women, Abi, Raeann and Vanessa went on a shopping spree. 30% of Abi's spending was equal to ¹₅ of Raeann's spending. Vanessa's spending was  50% more than Raeann's. If Raeann spent another $270, she would spend the same amount of money as Vanessa.

1. Find the ratio of Abi's spending to Raeann's to Vanessa's.
2. How much did Abi spend?

Abi	Raeann	Vanessa
2x2	3x2
	2x3	3x3
4 u	6 u	9 u

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

310 of Abi's spending = 15 of Raeann's spending
310 of Abi's spending =1x35x3 of Raeann's spending
310 of Abi's spending = 315 of Raeann's spending

Abi : Raeann
10 : 15
2 : 3

Vanessa's spending in percent when compared to Raeann's
= 100% + 50%
= 150%

Raeann : Vanessa
100 : 150
2 : 3

Raeann's spending is the repeated identity.  Make Raeann's spending the same.  LCM of 3 and 2 is 6.

Abi : Raeann : Vanessa
4 : 6 : 9

(b)

	Abi	Raeann	Vanessa
Before	4 u	6 u	9 u
Change		+ 3 u
After	4 u	9 u	9 u

Additional amount that Raeann would have to spend to be the same as Vanessa
= 9 u - 6 u
= 3 u

3 u = 270

1 u = 270 ÷ 3 = 90

Amount that Abi spent
= 4 u
= 4 x 90
= $360 

Answer(s): (a) 4 : 6 : 9; (b) $360