Three women, Opal, Penelope and Jane went on a shopping spree. 30% of Opal's spending was equal to ¹₂ of Penelope's spending. Jane's spending was  40% more than Penelope's. If Penelope spent another $180, she would spend the same amount of money as Jane.

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

Opal	Penelope	Jane
5x5	3x5
	5x3	7x3
25 u	15 u	21 u

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

310 of Opal's spending = 12 of Penelope's spending
310 of Opal's spending =1x32x3 of Penelope's spending
310 of Opal's spending = 36 of Penelope's spending

Opal : Penelope
10 : 6
5 : 3

Jane's spending in percent when compared to Penelope's
= 100% + 40%
= 140%

Penelope : Jane
100 : 140
5 : 7

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

Opal : Penelope : Jane
25 : 15 : 21

(b)

	Opal	Penelope	Jane
Before	25 u	15 u	21 u
Change		+ 6 u
After	25 u	21 u	21 u

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

6 u = 180

1 u = 180 ÷ 6 = 30

Amount that Opal spent
= 25 u
= 25 x 30
= $750 

Answer(s): (a) 25 : 15 : 21; (b) $750