Given the expression that models the tip amount for a total bill of $102:
[tex]0.25\mleft(102-x\mright)[/tex]
You know that "x" represents the dollar amount of the tax.
You also know that Mr. Jaxon tips $23.50.
Therefore, knowing all that information, you can set up the following equation to represent that situation:
[tex]23.50=0.25\mleft(102-x\mright)[/tex]
Now you have to solve for "x" in order to find its value:
[tex]\begin{gathered} 23.50=(0.25)(102)-(0.25)(x) \\ \\ 23.50=25.5-0.25x \end{gathered}[/tex][tex]\begin{gathered} 23.50-25.5=-0.25x \\ \\ -2=-0.25x \end{gathered}[/tex][tex]\begin{gathered} \frac{-2}{-0.25}=x \\ \\ x=8 \end{gathered}[/tex]
Hence, the answer is:
[tex]\text{ \$}8[/tex]
