Question

You and your friend are splitting a restaurant bill and leaving a tip. You pay half of the bill plus $5. Your friend pays half of the bill plus 25% of half the bill. You and your friend pay the same total amount. How much is half the bill?

Answer 1

$20

Explanation:

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

What you're trying to find = `1/2x`

`1/2x+5=a`
`1/2x+25%` of `1/2x=b`
`25%=1/4`

Since you and your friend pay the same total, `a=b`
If `a=b`,
`1/2x+5=1/2x+1/4(1/2x)`

First, you want to simplify.
`1/2x+5=1/2x+1/8x`

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

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

Remember, you're looking for HALF the bill, so it'd be `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.