Risa had $364 less than Luke. Risa spent ¹₄ of her money and Luke spent ³₅ of his money. In the end, Luke and Risa had the same amount of money left. Find the amount of money Luke had at first.

	Risa	Luke	Difference
Before	4x2 = 8 u	5x3 = 15 u	7 u
Change	- 1x2 = - 2 u	- 3x3 = - 9 u
After	3x2 = 6 u	2x3 = 6 u

Fraction of Risa's money left
= 1 - ¹₄
= ³₄

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

Luke and Risa had the same amount of money in the end. Make the numerators the same. LCM of 3 and 2 is 6.

³₄ of Risa's money = ²₅ of Luke's money
⁶₈ of Risa's money = ⁶₁₅ of Luke's money

Amount that Risa had at first = 8 u
Amount that Luke had at first = 15 u

Amount that Risa had less than Luke had at first
= 15 u - 8 u
= 7 u

7 u = 364

1 u = 364 ÷ 7 = 52

Amount that Luke had at first
= 15 u
= 15 x 52
= $780

Answer(s): $780