A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $38 and then an additional 4 cents per minute of use. In Plan B, the customer pays a monthly fee of $20 and then an additional 7 cents per minute of use.
For what amounts of monthly phone use will Plan A cost less than Plan B?
Use for m the number of minutes of phone use, and solve your inequality for m.
For Plan A, the cost equation is given by:
C(A) = 38 + 0.04m
For Plan B, the cost equation is given by:
C(B) = 20 + 0.07m
To find the amount of monthly phone use for which Plan A costs less than Plan B, we need to set up an inequality:
38 + 0.04m < 20 + 0.07m
Now we solve for m:
0.04m - 0.07m < 20 - 38
-0.03m < -18
m > -18 / -0.03
m > 600
Therefore, for monthly phone use greater than 600 minutes, Plan A will cost less than Plan B.
To determine the amount of monthly phone use for which Plan A costs less than Plan B, we need to compare the total cost for each plan.
For Plan A, the total cost can be represented by:
Cost_A = $38 + $0.04m (where m is the number of minutes of phone use)
For Plan B, the total cost can be represented by:
Cost_B = $20 + $0.07m
Now, we need to set up an inequality to find the value of m for which Cost_A is less than Cost_B.
Cost_A < Cost_B
$38 + $0.04m < $20 + $0.07m
$38 - $20 < $0.07m - $0.04m
$18 < $0.03m
To isolate m, divide both sides of the inequality by $0.03:
$18 / $0.03 < m
600 < m
Therefore, for monthly phone use greater than 600 minutes, Plan A will cost less than Plan B.
To determine for which amounts of monthly phone use Plan A costs less than Plan B, we need to compare the costs of the two plans based on the number of minutes of phone use (m).
First, let's set up the equation to represent the cost of Plan A:
Cost of Plan A = $38 (monthly fee) + 4 cents per minute of use = 38 + 0.04m
Next, let's set up the equation to represent the cost of Plan B:
Cost of Plan B = $20 (monthly fee) + 7 cents per minute of use = 20 + 0.07m
To find out when Plan A costs less than Plan B, we need to set up an inequality. Since we want Plan A to cost less, we'll use the "less than" symbol (<).
38 + 0.04m < 20 + 0.07m
Now, we can solve the inequality for m to find the range of monthly phone use where Plan A costs less than Plan B.
Let's start by isolating the variables on one side of the inequality:
38 - 20 < 0.07m - 0.04m
Now simplify the inequality:
18 < 0.03m
Divide both sides of the inequality by 0.03 to isolate m:
18/0.03 < m
Simplify the division:
600 < m
So, the inequality is m > 600.
Therefore, for any amount of monthly phone use (m) greater than 600 minutes, Plan A will cost less than Plan B.