Three women, Gillian, Usha and Nicole went on a shopping spree. 30% of Gillian's spending was equal to ¹₂ of Usha's spending. Nicole's spending was  25% more than Usha's. If Usha spent another $315, she would spend the same amount of money as Nicole.

1. Find the ratio of Gillian's spending to Usha's to Nicole's.
2. How much did Gillian spend?

Gillian	Usha	Nicole
5x4	3x4
	4x3	5x3
20 u	12 u	15 u

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

310 of Gillian's spending = 12 of Usha's spending
310 of Gillian's spending =1x32x3 of Usha's spending
310 of Gillian's spending = 36 of Usha's spending

Gillian : Usha
10 : 6
5 : 3

Nicole's spending in percent when compared to Usha's
= 100% + 25%
= 125%

Usha : Nicole
100 : 125
4 : 5

Usha's spending is the repeated identity.  Make Usha's spending the same.  LCM of 3 and 4 is 12.

Gillian : Usha : Nicole
20 : 12 : 15

(b)

	Gillian	Usha	Nicole
Before	20 u	12 u	15 u
Change		+ 3 u
After	20 u	15 u	15 u

Additional amount that Usha would have to spend to be the same as Nicole
= 15 u - 12 u
= 3 u

3 u = 315

1 u = 315 ÷ 3 = 105

Amount that Gillian spent
= 20 u
= 20 x 105
= $2100 

Answer(s): (a) 20 : 12 : 15; (b) $2100