Question

Members of the Lake Shawnee Club pay $40 per summer season plus$7.50 each time they rent a boat. Nonmembers pay $12.50 each timethey rent a boat. How many times would both a member and anonmember have to rent a boot in order to pay the same amounts

Answer 1

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.

Step-by-step 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:

`\begin{gathered} C_m=7.50x+40. \\ C_n=12.50y\text{.} \end{gathered}`

If they pay the same amounts, then:

`7.50x+40=12.50y\text{.}`

Solving for y:

`\begin{gathered} y=(7.50x)/(12.50)+(40)/(12.50)\text{.} \\ y=(3)/(5)x+(16)/(5.)\text{.} \end{gathered}`

Multiplying the last equation by 5 we get:

`5y=3x+16`

An integer solution to the above equation is x=3 and y=5.