Three women, Nicole, Jean and Jade went on a shopping spree. 30% of Nicole's spending was equal to ¹₅ of Jean's spending. Jade's spending was  40% more than Jean's. If Jean spent another $624, she would spend the same amount of money as Jade.

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

Nicole	Jean	Jade
2x5	3x5
	5x3	7x3
10 u	15 u	21 u

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

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

Nicole : Jean
10 : 15
2 : 3

Jade's spending in percent when compared to Jean's
= 100% + 40%
= 140%

Jean : Jade
100 : 140
5 : 7

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

Nicole : Jean : Jade
10 : 15 : 21

(b)

	Nicole	Jean	Jade
Before	10 u	15 u	21 u
Change		+ 6 u
After	10 u	21 u	21 u

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

6 u = 624

1 u = 624 ÷ 6 = 104

Amount that Nicole spent
= 10 u
= 10 x 104
= $1040 

Answer(s): (a) 10 : 15 : 21; (b) $1040