Linda had $1377 less than Fred. Linda spent ¹₆ of her money and Fred spent ⁴₇ of his money. In the end, Fred and Linda had the same amount of money left. Find the amount of money Fred had at first.

	Linda	Fred	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 Linda's money left
= 1 - ¹₆
= ⁵₆

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

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

⁵₆ of Linda's money = ³₇ of Fred's money
¹⁵₁₈ of Linda's money = ¹⁵₃₅ of Fred's money

Amount that Linda had at first = 18 u
Amount that Fred had at first = 35 u

Amount that Linda had less than Fred had at first
= 35 u - 18 u
= 17 u

17 u = 1377

1 u = 1377 ÷ 17 = 81

Amount that Fred had at first
= 35 u
= 35 x 81
= $2835

Answer(s): $2835