Three women, Penelope, Erika and Gem went on a shopping spree. 90% of Penelope's spending was equal to ¹₅ of Erika's spending. Gem's spending was  25% more than Erika's. If Erika spent another $819, she would spend the same amount of money as Gem.

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

Penelope	Erika	Gem
2x4	9x4
	4x9	5x9
8 u	36 u	45 u

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

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

Penelope : Erika
10 : 45
2 : 9

Gem's spending in percent when compared to Erika's
= 100% + 25%
= 125%

Erika : Gem
100 : 125
4 : 5

Erika's spending is the repeated identity.  Make Erika's spending the same.  LCM of 9 and 4 is 36.

Penelope : Erika : Gem
8 : 36 : 45

(b)

	Penelope	Erika	Gem
Before	8 u	36 u	45 u
Change		+ 9 u
After	8 u	45 u	45 u

Additional amount that Erika would have to spend to be the same as Gem
= 45 u - 36 u
= 9 u

9 u = 819

1 u = 819 ÷ 9 = 91

Amount that Penelope spent
= 8 u
= 8 x 91
= $728 

Answer(s): (a) 8 : 36 : 45; (b) $728