#### Explanation:

Lets put that question into an equation.
$a$ = Your Payment
$b$ = Your Friend's Payment
$x$ = Bill

What you're trying to find = $\frac{1}{2} x$

$\frac{1}{2} x + 5 = a$
1/2x+25% of $\frac{1}{2} x = b$
25%=1/4

Since you and your friend pay the same total, $a = b$
If $a = b$,
$\frac{1}{2} x + 5 = \frac{1}{2} x + \frac{1}{4} \left(\frac{1}{2} x\right)$

First, you want to simplify.
$\frac{1}{2} x + 5 = \frac{1}{2} x + \frac{1}{8} x$

Multiply by 8 on both sides to get rid of those fractions
$4 x + 40 = 4 x + x$

Subtract $4 x$ on both sides to find $x$
$40 = x$

Remember, you're looking for HALF the bill, so it'd be $\frac{1}{2}$ of x
Answer = $20$

This might be the wrong answer, since the question says that there is a tip. If the tip was not included in the equation, then I find \$20 to be half the bill.