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.