A pizza shop charges a flat delivery fee of $8 plus $12 for each pizza. If Marco's total bill, including the delivery fee, was $44, how many pizzas did Marco order?
For linear word problems with a flat fee plus a per-item charge, start by clearly defining a variable for the unknown quantity, then write an equation: fixed fee + (rate × quantity) = total. Solve the resulting two-step equation by isolating the variable (subtract the constant term from both sides, then divide by the coefficient). If unsure, plug each answer choice back into the cost expression to see which one matches the given total.
Hints
Define the variable
Decide what quantity you are trying to find. Let a variable represent the number of pizzas Marco ordered.
Write an equation for the total cost
Combine the flat delivery fee with the cost per pizza times the number of pizzas, and set this equal to the total bill of $44.
Solve the two-step equation
Once you have an equation, first undo the addition or subtraction, then undo the multiplication or division to isolate the variable.
Desmos Guide
Use Desmos to model the cost
In Desmos, type y = 8 + 12x to represent the total cost for pizzas, and on a new line type y = 44 to represent Marco’s total bill. Look at the point where the two lines intersect and read off the -value; that -value is the number of pizzas Marco ordered.
Step-by-step Explanation
Translate the situation into an equation
Identify the two parts of the bill:
- A flat delivery fee of $8 (this is a fixed amount)
- $12 for each pizza (this depends on how many pizzas are ordered)
Let be the number of pizzas Marco ordered. Then the total cost is modeled by the equation
because the delivery fee plus the cost of pizzas equals the total bill of $44.
Isolate the term with the variable
To solve , first get the term by itself.
Subtract 8 from both sides:
Now the equation is simpler: .
Solve for the number of pizzas
Now divide both sides of by 12 to solve for :
So Marco ordered pizzas, which corresponds to answer choice B.