Three women, Lynn, Diana and Penelope went on a shopping spree. 90% of Lynn's spending was equal to ¹₂ of Diana's spending. Penelope's spending was  50% more than Diana's. If Diana spent another $900, she would spend the same amount of money as Penelope.

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

Lynn	Diana	Penelope
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

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

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

Lynn : Diana
10 : 18
5 : 9

Penelope's spending in percent when compared to Diana's
= 100% + 50%
= 150%

Diana : Penelope
100 : 150
2 : 3

Diana's spending is the repeated identity.  Make Diana's spending the same.  LCM of 9 and 2 is 18.

Lynn : Diana : Penelope
10 : 18 : 27

(b)

	Lynn	Diana	Penelope
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

Additional amount that Diana would have to spend to be the same as Penelope
= 27 u - 18 u
= 9 u

9 u = 900

1 u = 900 ÷ 9 = 100

Amount that Lynn spent
= 10 u
= 10 x 100
= $1000 

Answer(s): (a) 10 : 18 : 27; (b) $1000