Answer: The number of times that a member has to rent a boat is 3 and a nonmember is 5 in order for them to pay the same amounts.
Explanation:
Let x be the number of times that a member rents a boat and y the number of times that a nonmember rents a boat, then we set the following equations:
[tex]\begin{gathered} C_m=7.50x+40. \\ C_n=12.50y\text{.} \end{gathered}[/tex]
If they pay the same amounts, then:
[tex]7.50x+40=12.50y\text{.}[/tex]
Solving for y:
[tex]\begin{gathered} y=\frac{7.50x}{12.50}+\frac{40}{12.50}\text{.} \\ y=\frac{3}{5}x+\frac{16}{5.}\text{.} \end{gathered}[/tex]
Multiplying the last equation by 5 we get:
[tex]5y=3x+16[/tex]
An integer solution to the above equation is x=3 and y=5.
