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We are told that the maximum amount to spend is $80 and that there is a 7.5% sales tax. If N is the amount we are going to spend then we need to have into account that we need to add the 7.5% of N and that should be at least equal to $80.
[tex]N+\frac{7.5}{100}N=80[/tex]Now we need to solve for N, to do that we add like terms:
[tex]\begin{gathered} (1+\frac{7.5}{100})N=80 \\ \frac{107.5}{100}N=80 \end{gathered}[/tex]Now we multiply both sides by 100:
[tex]107.5N=8000[/tex]Now we divide by 107.5:
[tex]N=\frac{8000}{107.5}[/tex]Solving the operations:
[tex]N=74.4\cong74[/tex]Therefore, the maximum amount to spend is $74