One phone company charges $12 per month plus $.05 per minute after the first 500 minutes. A second phone company charges $10 per month plus $.04 per minute after the first 300 minutes. How many minutes would a subscriber have to use so that the cost of the two plans is the same for a given month
you want x minutes, where
12+.05(x-500) = 10+.04(x-300)
x = 1100
To determine the number of minutes required for the cost of the two plans to be equal, let's define the variables and set up an equation.
Let:
- "x" be the number of minutes used in a given month.
- "C1" be the cost of the first phone company's plan.
- "C2" be the cost of the second phone company's plan.
For the first phone company, the cost can be calculated as follows:
C1 = $12 (base fee) + $0.05 (per minute charge) × (x - 500) (minutes over the first 500)
For the second phone company, the cost can be calculated as follows:
C2 = $10 (base fee) + $0.04 (per minute charge) × (x - 300) (minutes over the first 300)
We need to find the value of "x" when C1 = C2, so we can set up the equation:
$12 + $0.05(x - 500) = $10 + $0.04(x - 300)
Now, let's solve the equation.
$12 + $0.05x - $0.05(500) = $10 + $0.04x - $0.04(300)
$12 + $0.05x - $25 = $10 + $0.04x - $12
Combining like terms:
$0.05x - $0.05(500) = $0.04x - $0.04(300)
$0.05x - $25 = $0.04x - $12
Subtracting $0.04x and adding $25 to both sides:
$0.05x - $0.04x = - $12 + $25
$0.01x = $13
Dividing both sides by $0.01:
x = $13 ÷ $0.01
x = 1300
Therefore, a subscriber would have to use 1300 minutes for the cost of the two plans to be the same in a given month.