Three women, Jen, Mary and Lynn went on a shopping spree. 30% of Jen's spending was equal to ¹₆ of Mary's spending. Lynn's spending was  60% more than Mary's. If Mary spent another $3186, she would spend the same amount of money as Lynn.

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

Jen	Mary	Lynn
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Jen's spending is equal to ¹₆ of Mary's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Jen's spending = 16 of Mary's spending
310 of Jen's spending =1x36x3 of Mary's spending
310 of Jen's spending = 318 of Mary's spending

Jen : Mary
10 : 18
5 : 9

Lynn's spending in percent when compared to Mary's
= 100% + 60%
= 160%

Mary : Lynn
100 : 160
5 : 8

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

Jen : Mary : Lynn
25 : 45 : 72

(b)

	Jen	Mary	Lynn
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

Additional amount that Mary would have to spend to be the same as Lynn
= 72 u - 45 u
= 27 u

27 u = 3186

1 u = 3186 ÷ 27 = 118

Amount that Jen spent
= 25 u
= 25 x 118
= $2950 

Answer(s): (a) 25 : 45 : 72; (b) $2950