A gym charges a one-time registration fee of $25 and then $15 per month for membership. If Maria has paid a total of $175 so far, for how many months has she been a member?
For problems with a one-time fee plus a repeated monthly (or per-unit) cost, define a variable for the number of months or units, then write a simple linear equation: one-time fee + (per-month cost × number of months) = total paid. Solve by first subtracting the one-time fee from the total, then dividing by the monthly cost. Always distinguish clearly between fixed (one-time) and variable (per-month) charges to avoid including the fixed fee in the division.
Hints
Separate the one-time fee from the monthly cost
Think about which part of the total cost is paid only once and which part repeats every month. How can you remove the one-time part from the total?
Write an equation
Let be the number of months. Try to write an equation that adds the registration fee and the total monthly charges to equal 175.
Solve step by step
After you write the equation, first move the registration fee to the other side, then divide by the monthly fee to find .
Desmos Guide
Enter the total cost equation
In Desmos, type y = 25 + 15x to represent the total amount paid after months.
Represent the known total
On a new line, type y = 175 to show the horizontal line where the total cost is 175 dollars.
Find the intersection
Look for the point where the two graphs intersect and read off the -value of that point; that -value is the number of months Maria has been a member.
Step-by-step Explanation
Define the variable and write the equation
Let be the number of months Maria has been a member.
The total amount she has paid is the registration fee plus the monthly fees, so we can write the equation:
Here, 25 is the one-time fee, is the total monthly cost, and 175 is the total paid so far.
Isolate the monthly part of the cost
To solve for , first get by itself. Subtract 25 from both sides of the equation:
Now the equation tells you that 15 dollars per month times months equals 150 dollars.
Solve for the number of months
Now divide both sides of by 15 to get :
So Maria has been a member for 10 months, which corresponds to answer choice C.