Question

Fwam is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. Let C represent the total cost of using a computer for t minutes at the internet cafe. The table below has select values showing the linear relationship between t and C. Determine the number of minutes Fwam can use a computer if he only has $11.80 available to pay.

Answer 1

8.5 minutes

Explanation:

You want to know the time Fwam can use an internet cafe computer for $11.80 if the linear cost is $5.80 for 1 minute and $7.40 for 3 minutes.

Cost function

The slope of the cost function is ...

m = (C2 -C1)/(t2 -t1) = (7.40 -5.80)/(3 -1) = 1.60/2 = 0.80

Then the cost equation can be written in point-slope form as ...

C -5.80 = 0.80(t -1)

Time

We want to know the time (t) for a cost C = 11.80. Using that value in the cost function, we can solve for t:

11.80 -5.80 = 0.80(t -1)

6.00/0.80 = t -1

7.5 +1 = t

t = 8.5

Fwam can use the computer for 8.5 minutes if he can pay $11.80.