Question

The table shows the cost of Internet access at two different cafes. For how many hours of access is the cost at Cyber Station less than the cost at Web World?​

Answer 1

Any number of hours greater than 16

Explanation:

First thing we have to do is write each equation for each cafe's internet access. For Cyber Station, the rate is $1.50 per hour which is the slope of the line (slope is, after all, the rate of change of y to x...or here, cost to hours). The flat fee is what you are charged even if you use 0 hours. The linear equation for Cyber Station is y = 1.5x + 12

The linear equation for Web World, which only has a rate but no flat fee, is

y = 2.25x

We are asked for how many hours of access, x, is the cost, y, at Cyber Station LESS THAN the cost at Web World. That tells me that you are working with linear inequalities in class! We want the cost at CS to be less than that at WW so our inequality looks like this:

1.5x + 12 < 2.25x

Solving for x:

16 < x. That means, in words, that any number of hours over 16 will make Cyber Station cheaper to use than Web World.