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?

1 Answer
Nov 1, 2016

$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.