Let C be the cost per round and F be the fee to use the golf course.
When John plays 3 rounds of golf, he pays a total of F+3C.
When John plays 4 rounds of golf, he pays a total of F+4C.
Use these expressions to write down a system of equations, taking into account that John paid $50 to play 3 rounds and $60 to play 4 rounds:
[tex]\begin{gathered} F+3C=50 \\ F+4C=60 \end{gathered}[/tex]Solve this system using the elimination method. Substract the first equation from the second equation:
[tex]\begin{gathered} (F+4C)-(F+3C)=60-50 \\ \Rightarrow F+4C-F-3C=10 \\ \Rightarrow4C-3C+F-F=10 \\ \Rightarrow C+0=10 \\ \therefore C=10 \end{gathered}[/tex]Replace C=10 into the first equation to find the value of F:
[tex]\begin{gathered} F+3C=50 \\ \Rightarrow F+3(10)=50 \\ \Rightarrow F+30=50 \\ \Rightarrow F=50-30 \\ \therefore F=20 \end{gathered}[/tex]Therefore, the cost per round is $10 and the fee to use the golf course is $20.