How do I solve the following system?
x+y+z = 100
120x + 50y + 25z = 4000
where x, y, and z must all be at least one and are all integers. There will be more than one solution right
The Attempt at a Solution
I solved for z in terms of the other two variables and got z must be between 43 and 84. I choose p = 50 and then tried to solve for c but didn't get an integer. Is there a more systematic way to approach this question?