Three women, Lynn, Mary and Zoe went on a shopping spree. 90% of Lynn's spending was equal to ¹₂ of Mary's spending. Zoe's spending was  25% more than Mary's. If Mary spent another $378, she would spend the same amount of money as Zoe.

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

Lynn	Mary	Zoe
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Lynn's spending is equal to ¹₂ of Mary's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Lynn's spending = 12 of Mary's spending
910 of Lynn's spending =1x92x9 of Mary's spending
910 of Lynn's spending = 918 of Mary's spending

Lynn : Mary
10 : 18
5 : 9

Zoe's spending in percent when compared to Mary's
= 100% + 25%
= 125%

Mary : Zoe
100 : 125
4 : 5

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

Lynn : Mary : Zoe
20 : 36 : 45

(b)

	Lynn	Mary	Zoe
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

Additional amount that Mary would have to spend to be the same as Zoe
= 45 u - 36 u
= 9 u

9 u = 378

1 u = 378 ÷ 9 = 42

Amount that Lynn spent
= 20 u
= 20 x 42
= $840 

Answer(s): (a) 20 : 36 : 45; (b) $840