A ride-sharing service charges a flat booking fee of $2.50 plus $0.75 per mile. Mason’s credit card was charged $17.50 for a ride. How many miles did Mason travel?
For linear cost problems with a flat fee plus a per-unit charge, always write an equation in the form total cost = flat fee + (rate × quantity). Assign a variable to the unknown quantity (here, miles), plug in the known numbers, then solve the one-step-at-a-time: subtract the flat fee from both sides, and divide by the per-unit rate. Finally, do a quick check by substituting your result back into the original cost expression to confirm it matches the given total.
Hints
Set up the relationship
Ask yourself: What is being charged at a flat rate, and what is being charged per mile? Write an expression that combines both to equal the total cost.
Use a variable for miles
Let a variable (like ) represent the number of miles. How would you write the total ride cost using , , and ?
Undo the operations step by step
After you have the equation, first remove the flat fee by using the opposite operation. Then, to isolate the variable, use the opposite of multiplying by .
Check your result
Once you find a value for the miles, plug it back into the cost expression to see if it reproduces the total charge of 17.50.
Desmos Guide
Use Desmos to compute the miles directly
In Desmos, type the expression (17.5 - 2.5) / 0.75 and press Enter. The output value is the number of miles Mason traveled.
Step-by-step Explanation
Define the variable and write the equation
Let be the number of miles Mason traveled.
The ride cost is a flat fee plus a per-mile charge, so the total cost is:
This equation says: booking fee plus times miles equals the total charge .
Isolate the miles term
Subtract the flat booking fee from both sides to get the cost of just the miles:
Now represents the cost for the miles alone.
Solve for the number of miles
To find , divide both sides of the equation by :
Notice that , so dividing by is the same as multiplying by :
So Mason traveled 20 miles.