Penelope had $1313 less than Elijah. Penelope spent ¹₆ of her money and Elijah spent ³₅ of his money. In the end, Elijah and Penelope had the same amount of money left. Find the amount of money Elijah had at first.

	Penelope	Elijah	Difference
Before	6x2 = 12 u	5x5 = 25 u	13 u
Change	- 1x2 = - 2 u	- 3x5 = - 15 u
After	5x2 = 10 u	2x5 = 10 u

Fraction of Penelope's money left
= 1 - ¹₆
= ⁵₆

Fraction of Elijah's money left
= 1 - ³₅
= ²₅

Elijah and Penelope had the same amount of money in the end. Make the numerators the same. LCM of 5 and 2 is 10.

⁵₆ of Penelope's money = ²₅ of Elijah's money
¹⁰₁₂ of Penelope's money = ¹⁰₂₅ of Elijah's money

Amount that Penelope had at first = 12 u
Amount that Elijah had at first = 25 u

Amount that Penelope had less than Elijah had at first
= 25 u - 12 u
= 13 u

13 u = 1313

1 u = 1313 ÷ 13 = 101

Amount that Elijah had at first
= 25 u
= 25 x 101
= $2525

Answer(s): $2525