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?
To determine the possible number of calling minutes for a monthly cost between $28 and $40, we can use the given information on the cellphone plan.
Let's break down the cost of the cellphone plan based on the number of calling minutes:
1. The basic cellphone plan costs $20 per month for 60 calling minutes.
2. For any additional time beyond 60 minutes, there is an additional cost of $0.40 per minute.
Now, we need to determine the range of calling minutes that fall within the given cost range of at least $28 and at most $40.
Let's solve this problem step by step:
1. First, let's calculate the cost of the basic cellphone plan for 60 calling minutes. Since this plan costs $20 per month for 60 minutes, the cost is $20.
2. Next, we need to determine the additional cost for any minutes beyond the initial 60 minutes. Since the cost is $0.40 per minute, we can multiply the number of additional minutes (x - 60) by the cost per minute ($0.40) to find the additional cost. This can be expressed as: 0.40(x - 60).
3. To calculate the total monthly cost (C), we sum up the basic plan cost and the additional cost:
C = $20 + 0.40(x - 60).
4. Now, we need to solve the inequality that represents the given cost range: $28 ≤ C ≤ $40.
a. First, let's solve the lower bound of the inequality: $28 ≤ C.
Substitute the expression for C into the inequality:
$28 ≤ $20 + 0.40(x - 60).
Simplify the equation:
$28 ≤ $20 + 0.40x - 24.
Combine like terms:
$28 ≤ 0.40x - 4.
Add 4 to both sides of the equation to isolate the variable:
$32 ≤ 0.40x.
Divide both sides of the equation by 0.40 to solve for x:
x ≥ $32 ÷ 0.40.
x ≥ 80.
b. Next, let's solve the upper bound of the inequality: C ≤ $40.
Substitute the expression for C into the inequality:
$20 + 0.40(x - 60) ≤ $40.
Simplify the equation:
$20 + 0.40x - 24 ≤ $40.
Combine like terms:
-4 + 0.40x ≤ $40.
Add 4 to both sides of the equation to isolate the variable:
0.40x ≤ $44.
Divide both sides of the equation by 0.40 to solve for x:
x ≤ $44 ÷ 0.40.
x ≤ 110.
Thus, the possible number of calling minutes for a monthly cost of at least $28 and at most $40 is between 80 and 110 (inclusive).