Question 71·Medium·Linear Equations in One Variable
A customer paid a one-time sign-up fee of $25 and then $40 each month for a streaming service. The equation above represents the total amount, in dollars, the customer has paid after months. How many months has the customer had the streaming service?
For linear equations in one variable that come from word problems, first connect each part of the equation to the story (fixed fee, rate, total). Then solve algebraically by isolating the variable: undo any addition or subtraction first, then undo multiplication or division. Keep the operations balanced on both sides of the equation to avoid errors and quickly find the value of the variable.
Hints
Match the equation to the story
Identify which part of is the one-time fee and which part depends on the number of months.
Start isolating the variable
What operation will remove the from the left side so that only the term remains?
Finish solving for the number of months
After you have on one side, what should you do to both sides of the equation to get by itself?
Desmos Guide
Enter the expressions to graph
In Desmos, type y = 40x + 25 on one line and y = 265 on another line. These represent the total cost and the constant total of $265.
Find the intersection point
Look for the point where the two lines intersect. The x-coordinate of this intersection is the number of months that makes the total $265.
Step-by-step Explanation
Understand what each number represents
In the equation :
- $25 is the one-time sign-up fee.
- is the total paid for months at $40 per month.
- $265 is the total amount paid.
We want to solve for , the number of months.
Isolate the term with the variable
To begin solving for , subtract the fixed fee (25) from both sides of the equation so that only the monthly part remains on the left:
This simplifies to:
Solve for the variable
Now divide both sides of the equation by to get alone:
So:
Therefore, the customer has had the streaming service for 6 months.