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?

$20

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.