Question 136·Easy·Linear Equations in One Variable
A mobile phone plan charges a fixed monthly fee of $49.99 plus $0.15 for each text message sent. If Elena’s total charge last month was $64.39, how many text messages did she send?
For phone-plan and similar “fixed fee + per-use cost” problems, immediately write an equation of the form . Then subtract the fixed fee from the total to isolate the variable term, and divide by the per-unit rate to solve for . Work carefully with decimals (line up decimal points when subtracting, and if division feels tricky, convert dollars to cents) and always plug your solution back into the original expression to quickly verify it matches the given total.
Hints
Identify fixed and variable parts of the bill
One part of the bill stays the same every month, and one part depends on how many texts she sends. Which numbers in the problem represent these two parts?
Write an equation for the total charge
Let be the number of text messages. How can you write “fixed fee plus $0.15 for each text equals $64.39” as an equation in ?
Separate the text-message cost from the fixed fee
Once you have the equation, first remove the fixed monthly fee from the total by doing the same operation on both sides. What does that tell you about the total cost of the text messages?
Use unit rate to find the number of texts
You will know how many dollars came from texts and how many dollars each text costs. How do you find how many texts there were from that information?
Desmos Guide
Use Desmos to solve the equation numerically
In a new expression line, type (64.39 - 49.99) / 0.15 and press Enter. The value that Desmos outputs is the number of text messages Elena sent.
Step-by-step Explanation
Translate the situation into an equation
The total monthly charge is made of:
- a fixed fee of $49.99, plus
- $0.15 for each text message.
If is the number of text messages, the equation is:
This represents “fixed fee + (cost per text)(number of texts) = total charge.”
Isolate the text-message charge
To find how much of the bill came from text messages, subtract the fixed fee from both sides of the equation:
Now compute the difference:
So the total cost from texts is $14.40.
Solve for the number of text messages
Each text costs $0.15, and the total cost for texts is $14.40. To find the number of texts, divide the total text cost by the cost per text:
Carry out the division carefully (you can think in cents: 1440 cents divided by 15 cents per text).
Compute and check the solution
Compute the division:
So Elena sent text messages.
Check: , and , which matches the given total. Therefore, the correct answer is 96.