Ivory had $1978 less than John. Ivory spent ¹₆ of her money and John spent ⁵₇ of his money. In the end, John and Ivory had the same amount of money left. Find the amount of money John had at first.

	Ivory	John	Difference
Before	6x2 = 12 u	7x5 = 35 u	23 u
Change	- 1x2 = - 2 u	- 5x5 = - 25 u
After	5x2 = 10 u	2x5 = 10 u

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

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

John and Ivory had the same amount of money in the end. Make the numerators the same. LCM of 5 and 2 is 10.

⁵₆ of Ivory's money = ²₇ of John's money
¹⁰₁₂ of Ivory's money = ¹⁰₃₅ of John's money

Amount that Ivory had at first = 12 u
Amount that John had at first = 35 u

Amount that Ivory had less than John had at first
= 35 u - 12 u
= 23 u

23 u = 1978

1 u = 1978 ÷ 23 = 86

Amount that John had at first
= 35 u
= 35 x 86
= $3010

Answer(s): $3010