Three women, Olivia, Mary and Jean went on a shopping spree. 90% of Olivia's spending was equal to ¹₅ of Mary's spending. Jean's spending was  25% less than Mary's. If Mary spent $603 less, she would spend the same amount of money as Jean.

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

Olivia	Mary	Jean
2x4	9x4
	4x9	3x9
8 u	36 u	27 u

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

910 of Olivia's spending = 15 of Mary's spending
910 of Olivia's spending =1x95x9 of Mary's spending
910 of Olivia's spending = 945 of Mary's spending

Olivia : Mary
10 : 45
2 : 9

Jean's spending in percent when compared to Mary's
= 100% - 25%
= 75%

Mary : Jean
100 : 75
4 : 3

Mary's spending is the repeated identity.  Make Mary's spending the same.  LCM of 9 and 4 is 36.

Olivia : Mary : Jean
8 : 36 : 27

(b)

	Olivia	Mary	Jean
Before	8 u	36 u	27 u
Change		- 9 u
After	8 u	27 u	27 u

Additional amount that Mary would have to spend less to be the same as Jean
= 36 u - 27 u
= 9 u

9 u = 603

1 u = 603 ÷ 9 = 67

Amount that Jean spent
= 27 u
= 27 x 67
= $1809 

Answer(s): (a) 8 : 36 : 27; (b) $1809