Three women, Jen, Mary and Linda went on a shopping spree. 30% of Jen's spending was equal to ¹₂ of Mary's spending. Linda's spending was  40% more than Mary's. If Mary spent another $552, she would spend the same amount of money as Linda.

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

Jen	Mary	Linda
5x5	3x5
	5x3	7x3
25 u	15 u	21 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Jen's spending is equal to ¹₂ of Mary's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Jen's spending = 12 of Mary's spending
310 of Jen's spending =1x32x3 of Mary's spending
310 of Jen's spending = 36 of Mary's spending

Jen : Mary
10 : 6
5 : 3

Linda's spending in percent when compared to Mary's
= 100% + 40%
= 140%

Mary : Linda
100 : 140
5 : 7

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

Jen : Mary : Linda
25 : 15 : 21

(b)

	Jen	Mary	Linda
Before	25 u	15 u	21 u
Change		+ 6 u
After	25 u	21 u	21 u

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

6 u = 552

1 u = 552 ÷ 6 = 92

Amount that Jen spent
= 25 u
= 25 x 92
= $2300 

Answer(s): (a) 25 : 15 : 21; (b) $2300