Three women, Joelle, Nicole and Penelope went on a shopping spree. 90% of Joelle's spending was equal to ¹₅ of Nicole's spending. Penelope's spending was  70% less than Nicole's. If Nicole spent $3465 less, she would spend the same amount of money as Penelope.

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

Joelle	Nicole	Penelope
2x10	9x10
	10x9	3x9
20 u	90 u	27 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Joelle's spending is equal to ¹₅ of Nicole's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Joelle's spending = 15 of Nicole's spending
910 of Joelle's spending =1x95x9 of Nicole's spending
910 of Joelle's spending = 945 of Nicole's spending

Joelle : Nicole
10 : 45
2 : 9

Penelope's spending in percent when compared to Nicole's
= 100% - 70%
= 30%

Nicole : Penelope
100 : 30
10 : 3

Nicole's spending is the repeated identity.  Make Nicole's spending the same.  LCM of 9 and 10 is 90.

Joelle : Nicole : Penelope
20 : 90 : 27

(b)

	Joelle	Nicole	Penelope
Before	20 u	90 u	27 u
Change		- 63 u
After	20 u	27 u	27 u

Additional amount that Nicole would have to spend less to be the same as Penelope
= 90 u - 27 u
= 63 u

63 u = 3465

1 u = 3465 ÷ 63 = 55

Amount that Penelope spent
= 27 u
= 27 x 55
= $1485 

Answer(s): (a) 20 : 90 : 27; (b) $1485