By your cell phone contract, you pay a monthly fee plus $0.03 for each minute you spend on the phone. In one month, you spent 240 minutes over the phone, and had a bill totaling $26.20.
Let x be the number of minutes you spend on the phone in a month, and let y be your total cell phone bill for that month. Use a linear equation to model your monthly bill based on the number of minutes you spend on the phone.
a.) Slope intercept equation
b.)If you spend 150 minutes on the phone in a month, you would be billed?
c.) If your bill was $31.90 one month, you must have spent _____
minutes on the phone in that month.
a) To model the monthly bill based on the number of minutes spent on the phone, we can start by identifying the variables and their relationships.
Let x be the number of minutes spent on the phone in a month (independent variable), and y be the total cell phone bill for that month (dependent variable).
The monthly fee is a fixed amount, and it is not dependent on the number of minutes spent on the phone. Let's assume the monthly fee is denoted as a.
The additional charge for each minute spent on the phone is $0.03, so the relationship between the number of minutes (x) and the additional charge (b) is given by:
b = 0.03x
Hence, the linear equation to model the monthly bill based on the number of minutes spent on the phone is:
y = a + 0.03x
b) To find the bill if you spend 150 minutes on the phone in a month, substitute x = 150 into the equation:
y = a + 0.03(150)
Simplifying,
y = a + 4.5
So, if you spend 150 minutes on the phone in a month, you would be billed a + $4.5.
c) If the bill was $31.90 in one month, we can substitute y = 31.90 into the equation and solve for x:
31.90 = a + 0.03x
Since we don't have the value of the monthly fee (a), we cannot determine the exact number of minutes spent on the phone in that month without more information.
a) To model the monthly bill based on the number of minutes spent on the phone, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where y represents the total bill, x represents the number of minutes spent on the phone, m represents the cost per minute, and b represents the base monthly fee.
In this case, the base monthly fee is $26.20, and the additional cost per minute is $0.03. Therefore, we can rewrite the equation as:
y = 0.03x + 26.20
b) To find out the bill for spending 150 minutes on the phone, we can substitute x = 150 into the equation:
y = 0.03(150) + 26.20
y = 4.50 + 26.20
y = 30.70
Therefore, if you spend 150 minutes on the phone in a month, you would be billed $30.70.
c) To find the number of minutes spent on the phone if the bill was $31.90, we can rearrange the equation as follows:
y = 0.03x + 26.20
Now substitute y = 31.90 into the equation:
31.90 = 0.03x + 26.20
Next, subtract 26.20 from both sides:
31.90 - 26.20 = 0.03x
Simplifying:
5.70 = 0.03x
Finally, divide both sides by 0.03 to isolate x:
x = 5.70 / 0.03
x ≈ 190
Therefore, if your bill was $31.90 one month, you must have spent approximately 190 minutes on the phone in that month.
If the fee is f, then
y = f + .03x
You know that
f + .03*240 = 26.20
So, find f, and then use that to work the rest