Diana had $651 less than Luke. Diana spent ¹₇ of her money and Luke spent ⁴₇ of his money. In the end, Luke and Diana had the same amount of money left. Find the amount of money Luke had at first.

	Diana	Luke	Difference
Before	7x1 = 7 u	7x2 = 14 u	7 u
Change	- 1x1 = - 1 u	- 4x2 = - 8 u
After	6x1 = 6 u	3x2 = 6 u

Fraction of Diana's money left
= 1 - ¹₇
= ⁶₇

Fraction of Luke's money left
= 1 - ⁴₇
= ³₇

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

⁶₇ of Diana's money = ³₇ of Luke's money
⁶₇ of Diana's money = ⁶₁₄ of Luke's money

Amount that Diana had at first = 7 u
Amount that Luke had at first = 14 u

Amount that Diana had less than Luke had at first
= 14 u - 7 u
= 7 u

7 u = 651

1 u = 651 ÷ 7 = 93

Amount that Luke had at first
= 14 u
= 14 x 93
= $1302

Answer(s): $1302