Three women, Shannon, Marion and Jean went on a shopping spree. 90% of Shannon's spending was equal to ¹₅ of Marion's spending. Jean's spending was  60% less than Marion's. If Marion spent $621 less, she would spend the same amount of money as Jean.

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

Shannon	Marion	Jean
2x5	9x5
	5x9	2x9
10 u	45 u	18 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Shannon's spending is equal to ¹₅ of Marion's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Shannon's spending = 15 of Marion's spending
910 of Shannon's spending =1x95x9 of Marion's spending
910 of Shannon's spending = 945 of Marion's spending

Shannon : Marion
10 : 45
2 : 9

Jean's spending in percent when compared to Marion's
= 100% - 60%
= 40%

Marion : Jean
100 : 40
5 : 2

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

Shannon : Marion : Jean
10 : 45 : 18

(b)

	Shannon	Marion	Jean
Before	10 u	45 u	18 u
Change		- 27 u
After	10 u	18 u	18 u

Additional amount that Marion would have to spend less to be the same as Jean
= 45 u - 18 u
= 27 u

27 u = 621

1 u = 621 ÷ 27 = 23

Amount that Jean spent
= 18 u
= 18 x 23
= $414 

Answer(s): (a) 10 : 45 : 18; (b) $414