Need help setting up equation for a word problem

Question

The word problem is: "Corey the computer guy bought a number of old computers for \$$3600$. After fixing them up he sold them (except for three that couldn’t be salvaged) for \$$4050$, making a profit of \$$150$ on each computer he sold. How many computers did he sell?"

My work is as follows:

Let $n=$ number of computers; let $c=$ cost of a single computer

$n c= 3600\;$ and $c= 3600/n$

$(n-3)(c+150) = 4050;\; (n-3) (3600/n +150) = 4050$

And then after expanding and factoring, my final answer is $12,$ but the actual answer is $9$. Am I setting up the equation right? If not, what I am I doing wrong?

Answer 1

Continuing your work:

Multiply both sides by $n$:

$(n-3)(3600+150n)=4050n$

Dividing both sides by $150$:

$(n-3)(n+24)=27n$

$n^2+21n-72=27n$

$n^2-6n-72=0$

Factoring,

$(n-12)(n+6)=0$

$n=12$ or $n=-6$

$n$ is positive (you can't buy a negative amount of computers), so $n=12$.

So, the number of computers he sold is $n-3=12-3=9$.

Answer 2

What was $12$? Was $n=12$? When you defined $n$, did you define it as the number of computers sold (the quantity the question asks for), or something else?