A mechanical engineer bought 24 boxes of screws for P2200. There were three types of screws bough. Screw A cost P300 per box, screw B costs P150 per box and screw C costs P50 per box. How many boxes of each screw did he buy?

Question

ajprincess · Answer

Let the number of boxes of screw A be x ,  the number of boxes of screw B be y and the number of boxes of screw C be z.
Then
x+y+z=24
300x+150y+50z=2200
30x+15y+5z=220
6x+3y+z=44. I feel like some data is missing.

anonymous · Answer

Yeah, you'd expect there be a third equation...
There is some data that can help us narrow things down though.
For instance: $x, y, z \in \mathbb{N} $

anonymous · Answer

That would exclude 0.

anonymous · Answer

{x = 2, y = 5, z = 17} 
Solved @ajprincess' first two equations in 1/1000 sec using Mathematica's Constrained Optimization function, Maximize.

Refer to the attachment.