A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $35.70 and then an additional 6 cents per minute of use. In Plan B, the customer pays a monthly fee of $30 and then an additional 7 cents per minute of use.
For what amounts of monthly phone use will Plan A cost no more than Plan B?
Use m for the number of minutes of phone use, and solve your inequality for m.
.06 m + 37.50 ≤ .07 m + 30.00
7.50 ≤ .01 m
To determine the monthly phone use for which Plan A costs no more than Plan B, let's set up the inequality.
In Plan A, the cost is calculated as a monthly fee of $35.70 plus 6 cents per minute: $0.06m.
In Plan B, the cost is calculated as a monthly fee of $30 plus 7 cents per minute: $0.07m.
Thus, we can write the inequality as follows:
35.70 + 0.06m ≤ 30 + 0.07m
Now, let's solve the inequality for m:
35.70 - 30 ≤ 0.07m - 0.06m
5.70 ≤ 0.01m
Dividing both sides by 0.01:
570 ≤ m
Therefore, for monthly phone use of 570 minutes or less, Plan A costs no more than Plan B.
To find the range of monthly phone use (m) for which Plan A costs no more than Plan B, we need to compare the total cost of each plan given the monthly phone use.
For Plan A, the monthly cost is the sum of the fixed monthly fee ($35.70) and the additional cost per minute (6 cents or $0.06 multiplied by the number of minutes used, m). So the total cost of Plan A is:
Cost of Plan A = $35.70 + $0.06m
Plan B, on the other hand, has a fixed monthly fee of $30 and an additional cost per minute of 7 cents or $0.07 multiplied by the number of minutes used, m. The total cost of Plan B is:
Cost of Plan B = $30 + $0.07m
To determine when Plan A costs no more than Plan B, we need to find the range of m values for which the cost of Plan A is less than or equal to the cost of Plan B:
$35.70 + $0.06m ≤ $30 + $0.07m
To solve this inequality for m, we can start by isolating the terms involving m on one side of the equation:
$35.70 - $30 ≤ $0.07m - $0.06m
$5.70 ≤ $0.01m
Next, divide both sides of the inequality by $0.01 to solve for m:
$5.70 / $0.01 ≤ m
570 ≤ m
Therefore, for Plan A to cost no more than Plan B, the monthly phone use (m) should be equal to or greater than 570 minutes.