Three women, Zoe, Cathy and Xandra went on a shopping spree. 30% of Zoe's spending was equal to ¹₆ of Cathy's spending. Xandra's spending was  40% more than Cathy's. If Cathy spent another $1926, she would spend the same amount of money as Xandra.

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

Zoe	Cathy	Xandra
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

310 of Zoe's spending = 16 of Cathy's spending
310 of Zoe's spending =1x36x3 of Cathy's spending
310 of Zoe's spending = 318 of Cathy's spending

Zoe : Cathy
10 : 18
5 : 9

Xandra's spending in percent when compared to Cathy's
= 100% + 40%
= 140%

Cathy : Xandra
100 : 140
5 : 7

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

Zoe : Cathy : Xandra
25 : 45 : 63

(b)

	Zoe	Cathy	Xandra
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

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

18 u = 1926

1 u = 1926 ÷ 18 = 107

Amount that Zoe spent
= 25 u
= 25 x 107
= $2675 

Answer(s): (a) 25 : 45 : 63; (b) $2675