Question

By your cell phone contract, you pay a monthly fee plus $0.06 for each minute you spend on the phone. In one month, you spent 250 minutes over the phone, and had a bill totaling $32.00. 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, in dollars. Use a linear equation to model your monthly bill based on the number of minutes you spend on the phone. A. This line's slope-intercept equation is: B. If you spend 180 minutes on the phone in a month, you would be billed: C. If your bill was $41.60 one month, you must have spent [blank] minutes on the phone in that month.

Answer 1

Given, x be the number of minutes you spend on the phone in a month, and y be your total cell phone bill for that month, in dollars.

The slope intercept equation of a straight line is y=mx+c, where x is the independent variable, m is the slope of the line and c is the y intercept.

Since the fee charged for each minute is $0.06, the linear equation for the given case can be expressed as

y=0.06x+c ......(1)

Here, c is the monthly fee for using cell phone.

Given, $0.06 is to be paid for each minute.

Total time taken in minutes, x=250.

Total cell phone bill for that month, y=$32.00.

Substitute the values in equation (1) to find the monthly fee c.

$\begin{gathered} 32=0.06\times250+c \\ 32=15+c \\ 32-15=c \\ 17=c \end{gathered}$

Hence, the monthly fee is c=$17.

A) Now, the slope intercept equation for the given case is,

$y=0.06x+17$

B) If the number of minutes spend in phone is x=180, then the total bill can be found as,

$\begin{gathered} y=0.06\times180+17 \\ y=27.8 \end{gathered}$

Therefore, the total bill is $27.8 .

C) Given, total bill amount y=$41.60. Put the values in equation (1) to find x.

$\begin{gathered} 41.6=0.06\times x+17 \\ 41.6-17=0.06\times x \\ 24.6=0.06x \\ 410=x \end{gathered}$

Therefore, the number of minutes spend is 410.