Emily had $1302 less than Reggie. Emily spent ¹₇ of her money and Reggie spent ⁵₇ of his money. In the end, Reggie and Emily had the same amount of money left. Find the amount of money Reggie had at first.

	Emily	Reggie	Difference
Before	7x1 = 7 u	7x3 = 21 u	14 u
Change	- 1x1 = - 1 u	- 5x3 = - 15 u
After	6x1 = 6 u	2x3 = 6 u

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

Fraction of Reggie's money left
= 1 - ⁵₇
= ²₇

Reggie and Emily had the same amount of money in the end. Make the numerators the same. LCM of 6 and 2 is 6.

⁶₇ of Emily's money = ²₇ of Reggie's money
⁶₇ of Emily's money = ⁶₂₁ of Reggie's money

Amount that Emily had at first = 7 u
Amount that Reggie had at first = 21 u

Amount that Emily had less than Reggie had at first
= 21 u - 7 u
= 14 u

14 u = 1302

1 u = 1302 ÷ 14 = 93

Amount that Reggie had at first
= 21 u
= 21 x 93
= $1953

Answer(s): $1953