At first, Daniel, John and Liam had the same amount of money. After Liam spent some of his money, Daniel spent ²₇ of his money and John spent ¹₂ of his money, Daniel had $45 more than John. In the end, the total amount of money the three boys had left was $386. How much money did Liam spend?

	Daniel	John	Liam	Total
Before	7x2 =  14 u	2x7 = 14 u	14 u
Change	- 2x2 = - 4 u	- 1x7 = - 7 u	- ?
After	5x2 = 10 u	1x7 = 7 u		$386

The amount that Daniel and John each had at first is the same.  Make the amount that they each had the same.  LCM of 7 and 2 is 14.

Amount that Daniel had more than John in the end
= 10 u - 7 u
= 3 u

3 u = 45

1 u = 45 ÷ 3 = 15

Amount that Daniel and John had in the end
= 10 u + 7 u
= 17 u
= 17 x 15
= $255

Amount that Liam had in the end
= 386 - 255
= $131

Amount that Liam had at first
= 14 u
= 14 x 15
= $210

Amount that Liam spent
= 210 - 131
= $79

Answer(s): $79