Three women, Penelope, Natalie and Nora went on a shopping spree. 30% of Penelope's spending was equal to ¹₅ of Natalie's spending. Nora's spending was  50% more than Natalie's. If Natalie spent another $132, she would spend the same amount of money as Nora.

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

Penelope	Natalie	Nora
2x2	3x2
	2x3	3x3
4 u	6 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Penelope's spending is equal to ¹₅ of Natalie's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Penelope's spending = 15 of Natalie's spending
310 of Penelope's spending =1x35x3 of Natalie's spending
310 of Penelope's spending = 315 of Natalie's spending

Penelope : Natalie
10 : 15
2 : 3

Nora's spending in percent when compared to Natalie's
= 100% + 50%
= 150%

Natalie : Nora
100 : 150
2 : 3

Natalie's spending is the repeated identity.  Make Natalie's spending the same.  LCM of 3 and 2 is 6.

Penelope : Natalie : Nora
4 : 6 : 9

(b)

	Penelope	Natalie	Nora
Before	4 u	6 u	9 u
Change		+ 3 u
After	4 u	9 u	9 u

Additional amount that Natalie would have to spend to be the same as Nora
= 9 u - 6 u
= 3 u

3 u = 132

1 u = 132 ÷ 3 = 44

Amount that Penelope spent
= 4 u
= 4 x 44
= $176 

Answer(s): (a) 4 : 6 : 9; (b) $176