Bryce bought 32 stools that required assembly from Need-A-Seat. Some stools have three legs, and the other stools have four legs. The box arrived with 108 stool legs. If the four-legged stools cost $20 and the three-legged stools cost $15, how much did all of Bryce’s stools cost?
Let x be the number of three-legged stools.
Thus, Bryce bought 32 - x four-legged stools.
The total cost of the three-legged stools is x * $15 = $<<x*15=15x>>15x.
The total cost of the four-legged stools is (32 - x) * $20 = $<<32-x=32-x>>20(32 - x) = $<<20*(32-x)=640-20x>>640 - 20x.
The four-legged stools have (32 - x) * 4 = 128 - 4x legs.
Thus, the cost equation becomes $15x + $20(108 - (128 - 4x)).
This means $15x + $20(108 - 128 + 4x) = $15x + $20(12x - 20) = $15x + $240x - $400 = $255x - $400.
Thus, $255x - $400 = 0.
Thus, $255x = $400.
Thus, x = $400 / $255 = 20 / 17 = 20/17 * 100/100 = 4000/1700.
Thus, x = 40/17.
This means x * $15 = 40/17 * $15 = 40 / 17 * 15 / 1 = 600/17.
Therefore, all of Bryce's stools cost $600/17 + $240(40/17 - 1) = $600/17 + $240(23/17) = $600/17 + $240*23 / 17 = $600/17 + $5520/17 = $6120/17.
This means all of Bryce’s stools cost $<<6120/17=360>>360. Answer: \boxed{360}.