An analytical lab costs $3.50$ dollars to run a sample and has $8430$ dollars per week for overhead. If it charges $32.75$ dollars a sample, what is the minimum amount of samples run to reach a profit?
My solution:
$3.50x+8430=32.75x$
$32.75x-3.5x=8430$
$x=288.2$
The lab must run at least 289 samples.
Is this the standard approach or would there be a better way to solve this problem?
Your approach is great! Just one minor notation thing: If I were solving this, I would use an inequality instead of an equation. $$32.75x - 3.50x - 8430 > 0 $$ $$x > 288.205...$$
This makes it a little easier for others reading your work to understand what you're solving for :)