Three women, Gwen, Shannon and Olivia went on a shopping spree. 30% of Gwen's spending was equal to ¹₆ of Shannon's spending. Olivia's spending was  50% more than Shannon's. If Shannon spent another $423, she would spend the same amount of money as Olivia.

1. Find the ratio of Gwen's spending to Shannon's to Olivia's.
2. How much did Gwen spend?

Gwen	Shannon	Olivia
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

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

310 of Gwen's spending = 16 of Shannon's spending
310 of Gwen's spending =1x36x3 of Shannon's spending
310 of Gwen's spending = 318 of Shannon's spending

Gwen : Shannon
10 : 18
5 : 9

Olivia's spending in percent when compared to Shannon's
= 100% + 50%
= 150%

Shannon : Olivia
100 : 150
2 : 3

Shannon's spending is the repeated identity.  Make Shannon's spending the same.  LCM of 9 and 2 is 18.

Gwen : Shannon : Olivia
10 : 18 : 27

(b)

	Gwen	Shannon	Olivia
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

Additional amount that Shannon would have to spend to be the same as Olivia
= 27 u - 18 u
= 9 u

9 u = 423

1 u = 423 ÷ 9 = 47

Amount that Gwen spent
= 10 u
= 10 x 47
= $470 

Answer(s): (a) 10 : 18 : 27; (b) $470