# Question #f669d

Jun 24, 2017

$x = 8$

#### Explanation:

I'm assuming the function $p \left(x\right)$ represents profit, which equals income minus cost. Therefore,

$p \left(x\right) = r \left(x\right) - c \left(x\right)$

$p \left(x\right) = \left(15 x\right) - \left(80 + 5 x\right)$

$p \left(x\right) = 10 x - 80$

Now, we need to find $x$ when $p \left(x\right) = 0$. To do this, we substitute $0$ for $p \left(x\right)$ and solve:

$0 = 10 x - 80$

$80 = 10 x$

$8 = x$

So the students will need to sell 8 shirts to break even.