The New network cell phone company charges $20 a month for service and $0.02 per minute of talking time. The mobile company charges $15 a month for service and $0.03 per minute of talking time..
(q) write expressions for the total bill of each company (1%).
2) set up an inequality that can be used to determine for what amount of time (in minutes) My mobile is the better plan. (1%).
3) solve your inequality (2%)
4) why did you have to put a restriction on the algebraic solution form part C? (1%).
1. Y = 20 + 0.02x.
Y = 15 + 0.03x.
x = minutes used.
2. 15 + 0.03x < 20 + 0.02x.
3. 0.03x - 0.02x < 20 - 15,
0.01x < 5,
X < 500 minutes.
cost1 = .02m + 25
cost2 = .03m + 15
when is cost2 < cost1 ?
.03m + 15 < .02m + 25
.01m < 10
m < 1000 , so for any time less than 1000 minutes, the second plan is cheaper
1) Expressions for the total bill of each company:
For New Network:
Total Bill = $20 + (0.02 * minutes of talking time)
For My Mobile:
Total Bill = $15 + (0.03 * minutes of talking time)
2) Inequality to determine for what amount of time My Mobile is the better plan:
$15 + (0.03 * minutes of talking time) < $20 + (0.02 * minutes of talking time)
3) Solving the inequality:
$15 + 0.03t < $20 + 0.02t
0.03t - 0.02t < $20 - $15
0.01t < $5
t < $5 / 0.01
t < 500 minutes
Therefore, for talking times less than 500 minutes, My Mobile is the better plan.
4) The restriction is put on the algebraic solution because we are dealing with minutes of talking time, which cannot be negative or a fraction. It doesn't make sense to have a negative or fractional amount of time. Therefore, we only consider the solution where the talking time is less than 500 minutes.
1) Expressions for the total bill of each company, given a certain amount of minutes, can be written as follows:
- For the New network cell phone company:
Total bill = $20 + ($0.02 * number of minutes)
- For the mobile company:
Total bill = $15 + ($0.03 * number of minutes)
2) To set up an inequality that can be used to determine for what amount of time (in minutes) the mobile company is the better plan, we need to compare the total bills of both companies. Let "x" represent the amount of time (in minutes). The inequality can be written as:
$15 + ($0.03 * x) < $20 + ($0.02 * x)
Here, the left side represents the total bill for the mobile company, and the right side represents the total bill for the New network cell phone company. We want to find the range of values for "x" where the mobile company's bill is less than the New network's bill.
3) Solving the inequality can help us determine the range of minutes where the mobile company's plan is cheaper. Let's solve it:
$15 + ($0.03 * x) < $20 + ($0.02 * x)
First, simplify the equation by combining like terms:
$15 - $20 < ($0.02 * x) - ($0.03 * x)
-$5 < -$0.01 * x
Now, divide both sides of the inequality by -0.01 (a negative number, so the inequality direction flips):
(-$5) / (-0.01) > x
500 > x
This means that for any amount of minutes less than 500, the mobile company's plan will be cheaper than the New network's plan.
4) The restriction on the algebraic solution in part 3 is to ensure that the inequality represents a valid scenario. In this case, minutes cannot be negative, so we excluded negative values. Additionally, we may want to consider practical constraints, such as the fact that people typically do not talk for excessively long periods of time, which would not make sense to include in the comparison.