basic cellphone plan cost $20 per month for 60 calling minutes. Additional time costs .40 per minute. The formula gives the monthly cost for this plan C, for x calling minutes, where x > 60. How many calling minutes are possible for a monthly cost of at least $28 and at most $40?
20 + .40(x-60) = C
Insert cost and solve for minutes(x).
A basic cellphone plan costs $20 per month for 60 calling minutes. Additional time costs $0.40 per minute. The formula 𝐶 = 20+0.40 (𝑥 −60) gives the monthly cost for this plan, C, for 𝑥 calling minutes, where 𝑥 > 60. How many calling minutes are possible for a monthly cost of at least $28 and at most $40?
To determine the range of calling minutes for a monthly cost between $28 and $40, we need to find the values of x that satisfy the cost formula.
Let's break down the cost formula:
- The basic plan cost is fixed at $20 per month for 60 calling minutes.
- For any additional minutes beyond the initial 60, the cost is $0.40 per minute.
So the formula for the monthly cost C, for x calling minutes, where x > 60, can be expressed as:
C = $20 + ($0.40 * (x - 60))
Now, we need to solve this formula for x when the cost C is between $28 and $40.
First, let's find the minimum value of x for a monthly cost of $28:
$28 = $20 + ($0.40 * (x - 60))
Simplifying the equation:
$8 = $0.40 * (x - 60)
20 = x - 60
x = 80
The minimum number of calling minutes for a monthly cost of $28 is 80.
Now, let's find the maximum value of x for a monthly cost of $40:
$40 = $20 + ($0.40 * (x - 60))
Simplifying the equation:
$20 = $0.40 * (x - 60)
50 = x - 60
x = 110
The maximum number of calling minutes for a monthly cost of $40 is 110.
Therefore, the possible range for calling minutes for a monthly cost between $28 and $40 is from 80 to 110 minutes.