Lucy had $312 less than Ivan. Lucy spent ¹₇ of her money and Ivan spent ³₅ of his money. In the end, Ivan and Lucy had the same amount of money left. Find the amount of money Ivan had at first.

	Lucy	Ivan	Difference
Before	7x1 = 7 u	5x3 = 15 u	8 u
Change	- 1x1 = - 1 u	- 3x3 = - 9 u
After	6x1 = 6 u	2x3 = 6 u

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

Fraction of Ivan's money left
= 1 - ³₅
= ²₅

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

⁶₇ of Lucy's money = ²₅ of Ivan's money
⁶₇ of Lucy's money = ⁶₁₅ of Ivan's money

Amount that Lucy had at first = 7 u
Amount that Ivan had at first = 15 u

Amount that Lucy had less than Ivan had at first
= 15 u - 7 u
= 8 u

8 u = 312

1 u = 312 ÷ 8 = 39

Amount that Ivan had at first
= 15 u
= 15 x 39
= $585

Answer(s): $585