Winnie had $1003 less than Bryan. Winnie spent ¹₆ of her money and Bryan spent ⁴₇ of his money. In the end, Bryan and Winnie had the same amount of money left. Find the amount of money Bryan had at first.

	Winnie	Bryan	Difference
Before	6x3 = 18 u	7x5 = 35 u	17 u
Change	- 1x3 = - 3 u	- 4x5 = - 20 u
After	5x3 = 15 u	3x5 = 15 u

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

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

Bryan and Winnie had the same amount of money in the end. Make the numerators the same. LCM of 5 and 3 is 15.

⁵₆ of Winnie's money = ³₇ of Bryan's money
¹⁵₁₈ of Winnie's money = ¹⁵₃₅ of Bryan's money

Amount that Winnie had at first = 18 u
Amount that Bryan had at first = 35 u

Amount that Winnie had less than Bryan had at first
= 35 u - 18 u
= 17 u

17 u = 1003

1 u = 1003 ÷ 17 = 59

Amount that Bryan had at first
= 35 u
= 35 x 59
= $2065

Answer(s): $2065