Question

The phone company A Fee and Fee has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 320 minutes, the monthly cost will be $166. If the customer uses 520 minutes, the monthly cost will be $246. A) Find an equation in the form y = m+b, where z is the number of monthly minutes used and y is the total monthly of the A Fee and Fee plan. Answer: y Do not use any commas in your answer. B) Use your equation to find the total monthly cost if 644 minutes are used.

Answer 1

A) Let's use the slope-intercept form of a linear equation: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

We know that when the number of minutes used is 320, the monthly cost is $166$. So we can plug those values into the equation and solve for $b$:

$166 = 320m + b$

We also know that when the number of minutes used is 520, the monthly cost is $246$. So we can plug those values into the equation and solve for $b$ again:

$246 = 520m + b$

Now we have two equations with two unknowns:

$166 = 320m + b$

$246 = 520m + b$

We can subtract the first equation from the second equation to eliminate $b$:

$246 - 166 = 520m + b - (320m + b)$

$80 = 200m$

$m = \frac{80}{200} = 0.4$

Now we can plug $m$ into one of the original equations to solve for $b$:

$166 = 320(0.4) + b$

$b = 166 - 128 = 38$

So the equation that represents the monthly cost ($y$) based on the number of monthly minutes used ($z$) is:

$y = 0.4z + 38$

B) To find the monthly cost for 450 minutes, we can plug $z = 450$ into the equation we just found:

$y = 0.4(450) + 38$

$y = 180 + 38$

$y = 218$

So the monthly cost for 450 minutes is $218.