Question 14·Medium·Linear Equations in One Variable
A bookstore sells folders for the same price each. A student buys 12 folders and one binder that costs $5, paying a total of $53 before tax.
What is the price, in dollars, of one folder?
(Express the answer as an integer)
For linear word problems like this, always start by defining a variable for the unknown quantity (here, the price of one folder). Translate each part of the story into algebra: multiply the variable by the number of identical items, add any fixed extra costs, and set this equal to the total. Then solve the resulting one-step or two-step linear equation carefully, doing inverse operations in order (undo addition/subtraction, then undo multiplication/division). This systematic approach helps avoid mixing up what to add, subtract, or divide and keeps the work quick and organized under time pressure.
Hints
Set up a variable
Let represent the price of one folder in dollars. How can you express the total cost of 12 folders using ?
Write the total cost equation
Combine the cost of 12 folders and the $5 binder. Set this equal to the total cost of $53 before tax.
Solve step by step
First, remove the binder’s $5 cost from the total. Then, use division to find the value of .
Desmos Guide
Compute the folder price directly
In Desmos, type (53 - 5) / 12 and press Enter. The numerical result shown is the price of one folder in dollars.
Step-by-step Explanation
Define the variable
Let be the price, in dollars, of one folder.
Write an equation for the total cost
The student buys 12 folders and one binder that costs $5, and the total is $53.
So the total cost in terms of is:
Isolate the folder term
Subtract 5 from both sides of the equation to remove the binder’s cost:
Solve for the price of one folder
Now divide both sides by 12 to solve for :
So the price of one folder is $4.