Question 62·Medium·Linear Functions
An amusement park charges an entry fee of $15 plus $4 for each ride. If Sasha spent $47 in total at the park, how many rides did she go on?
(Express the answer as an integer)
For word problems that involve a fixed fee plus a per-item cost, quickly translate the situation into an equation of the form (fixed amount) + (rate × number of items) = total. Define a clear variable for the quantity asked for, plug values into this structure, and then solve the resulting linear equation by isolating the variable—usually subtract the fixed fee first, then divide by the per-item cost. Always check that your answer makes sense by mentally recomputing the total cost.
Hints
Represent the situation with an equation
Try letting be the number of rides Sasha went on. How would you write an expression for the total cost using the entry fee of $15 and $4 per ride?
Include both the entry fee and the rides
Your expression should add the fixed $15 entry fee and the cost for rides at $4 each. Set this sum equal to the total amount Sasha spent, $47.
Solve the equation step by step
Once you have the equation, first subtract 15 from both sides, then divide by 4 to find .
Desmos Guide
Enter the cost equation
In Desmos, type y = 15 + 4x to represent the total cost as a function of the number of rides .
Show the total amount spent
On a new line, type y = 47 to represent Sasha’s total spending as a horizontal line.
Find the number of rides
Look at the point where the line intersects the line . The -coordinate of this intersection is the number of rides Sasha went on.
Step-by-step Explanation
Define the variable and write the equation
Let be the number of rides Sasha went on.
The park charges a fixed entry fee of $15 and $4 for each ride, so the total cost is:
This equation says: entry fee plus cost for rides equals the total Sasha spent, $47.
Isolate the term with the variable
Start solving the equation by subtracting 15 from both sides to move the entry fee to the other side:
Now simplify .
Solve for the variable
Compute the subtraction:
Now divide both sides by 4 to solve for :
This fraction simplifies to , so Sasha went on 8 rides.