Answer :
Katrina makes four exams, but since the score she makes on last one counts as two, the formula of the average value would be like this:
[tex]\text{Sav}=\frac{s1+s2+s3+s4+s4}{5}=\frac{s1+s2+s3+2\times s4}{5}[/tex]Now that we have the formula that relates the score of the last exam (s4) and the average score (sav), we can solve for s4, like this:
[tex]\begin{gathered} sav=\frac{s1+s2+s3+2\times s4}{5} \\ sav\times5=\frac{s1+s2+s3+2\times s4}{5}\times5 \\ sav\times5=s1+s2+s3+2\times s4 \\ sav\times5-s1-s2-s3=2\times s4 \\ \frac{sav\times5-s1-s2-s3}{2}=\frac{2}{2}\times s4 \\ s4=\frac{sav\times5-s1-s2-s3}{2} \end{gathered}[/tex]Now, let's replace the known values so we can find the value of s4:
[tex]\begin{gathered} s4=\frac{71\times5-74-83-86}{2} \\ s4=\frac{355-74-83-86}{2}=\frac{112}{2}=56 \end{gathered}[/tex]Then, Katrina must make more than 56 on the final test