Three women, Penelope, Gem and Winnie went on a shopping spree. 90% of Penelope's spending was equal to ¹₅ of Gem's spending. Winnie's spending was  70% less than Gem's. If Gem spent $4788 less, she would spend the same amount of money as Winnie.

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

Penelope	Gem	Winnie
2x10	9x10
	10x9	3x9
20 u	90 u	27 u

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

910 of Penelope's spending = 15 of Gem's spending
910 of Penelope's spending =1x95x9 of Gem's spending
910 of Penelope's spending = 945 of Gem's spending

Penelope : Gem
10 : 45
2 : 9

Winnie's spending in percent when compared to Gem's
= 100% - 70%
= 30%

Gem : Winnie
100 : 30
10 : 3

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

Penelope : Gem : Winnie
20 : 90 : 27

(b)

	Penelope	Gem	Winnie
Before	20 u	90 u	27 u
Change		- 63 u
After	20 u	27 u	27 u

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

63 u = 4788

1 u = 4788 ÷ 63 = 76

Amount that Winnie spent
= 27 u
= 27 x 76
= $2052 

Answer(s): (a) 20 : 90 : 27; (b) $2052