Question

On Chatty Cathy’s cell phone plan she pays for minutes used plus a fixed monthly charge. For 500 minutes she pays $35 total, and for 1500 minutes used she pays $55 total.

What is her monthly fixed charge?

Answer 1

We are given : For 500 minutes she pays $35 total and for 1500 minutes used she pays $55 total.

So, we can put the given information in form of two coordinates :

( Number of minutes, Total amount).

(500, 35) and (1500, 55).

First we need to find the slope between those two coordinates.

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(500,\:35\right),\:\left(x_2,\:y_2\right)=\left(1500,\:55\right)`

`m=(55-35)/(1500-500)`

`m=(1)/(50)`

Now applying slope-intercept form y=mx+b, where m is the slope and b is y-intercept.

y-intercept represents monthly fixed charge.

Plugging (x,y) = (500, 35) and slope m= 1/50 in slope-intercept form y=mx+b.

35 = 1/50 (500) +b

35 = 10 + b.

Subtracting 10 from both sides, we get

35-10 = 10-10 + b

b = 25.

Therefore, her monthly fixed charge is $25.