Three women, Sabrina, Nicole and Yen went on a shopping spree. 30% of Sabrina's spending was equal to ¹₅ of Nicole's spending. Yen's spending was  40% more than Nicole's. If Nicole spent another $426, she would spend the same amount of money as Yen.

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

Sabrina	Nicole	Yen
2x5	3x5
	5x3	7x3
10 u	15 u	21 u

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

310 of Sabrina's spending = 15 of Nicole's spending
310 of Sabrina's spending =1x35x3 of Nicole's spending
310 of Sabrina's spending = 315 of Nicole's spending

Sabrina : Nicole
10 : 15
2 : 3

Yen's spending in percent when compared to Nicole's
= 100% + 40%
= 140%

Nicole : Yen
100 : 140
5 : 7

Nicole's spending is the repeated identity.  Make Nicole's spending the same.  LCM of 3 and 5 is 15.

Sabrina : Nicole : Yen
10 : 15 : 21

(b)

	Sabrina	Nicole	Yen
Before	10 u	15 u	21 u
Change		+ 6 u
After	10 u	21 u	21 u

Additional amount that Nicole would have to spend to be the same as Yen
= 21 u - 15 u
= 6 u

6 u = 426

1 u = 426 ÷ 6 = 71

Amount that Sabrina spent
= 10 u
= 10 x 71
= $710 

Answer(s): (a) 10 : 15 : 21; (b) $710