Two phone companies offer discount rates to students.
The first company wants $9.95 per month plus $.10 per minute for long distance calls.
The second company wants $12.95 per month plus $.08 per minute for long distance calls.
Write a linear equation describing the total cost, y, for x minutes of long distance calls from Company 1.
Write a linear equation describing the total cost, y, for x minutes of long distance calls from Company 2.
How many minutes of long-distance calls would it take for the cost of long-distance for both offers to be the same?
Which method did you use to solve this problem?
9.95 + .10m = 12.95 + .08m
Solve for m.
To write a linear equation for the total cost, y, for x minutes of long distance calls from Company 1, we need to consider the fixed monthly charge and the charge per minute for long distance calls.
The fixed monthly charge for Company 1 is $9.95, and the charge per minute for long distance calls is $0.10. Therefore, the equation for Company 1's total cost can be written as:
y = 0.10x + 9.95
Similarly, to write a linear equation for the total cost, y, for x minutes of long distance calls from Company 2, we consider the fixed monthly charge and the charge per minute:
The fixed monthly charge for Company 2 is $12.95, and the charge per minute for long distance calls is $0.08. Hence, the equation for Company 2's total cost can be written as:
y = 0.08x + 12.95
To find the number of minutes of long-distance calls for the cost to be the same for both offers, we equate the two equations:
0.10x + 9.95 = 0.08x + 12.95
Solving this equation, we can find the value of x, which represents the number of minutes of long-distance calls that will make the costs equal.
In this case, we would subtract 0.08x from both sides of the equation to isolate the x term:
0.10x - 0.08x + 9.95 - 12.95 = 0
Simplifying further:
0.02x - 3 = 0
Now, add 3 to both sides of the equation to isolate the x term:
0.02x = 3
Finally, divide both sides of the equation by 0.02 to solve for x:
x = 3 / 0.02
Using a calculator, we find that x ≈ 150. Hence, it would take approximately 150 minutes of long-distance calls for the cost to be the same for both offers.
This problem was solved using the method of setting the equations for the total cost of both companies equal to each other and then solving for x.