Abi had $198 less than Fred. Abi spent ¹₅ of her money and Fred spent ⁵₇ of his money. In the end, Fred and Abi had the same amount of money left. Find the amount of money Fred had at first.

	Abi	Fred	Difference
Before	5x1 = 5 u	7x2 = 14 u	9 u
Change	- 1x1 = - 1 u	- 5x2 = - 10 u
After	4x1 = 4 u	2x2 = 4 u

Fraction of Abi's money left
= 1 - ¹₅
= ⁴₅

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

Fred and Abi had the same amount of money in the end. Make the numerators the same. LCM of 4 and 2 is 4.

⁴₅ of Abi's money = ²₇ of Fred's money
⁴₅ of Abi's money = ⁴₁₄ of Fred's money

Amount that Abi had at first = 5 u
Amount that Fred had at first = 14 u

Amount that Abi had less than Fred had at first
= 14 u - 5 u
= 9 u

9 u = 198

1 u = 198 ÷ 9 = 22

Amount that Fred had at first
= 14 u
= 14 x 22
= $308

Answer(s): $308