algebra - blowing my mind!

Question

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 6

cents per minute of use. In Plan B, the customer pays a monthly fee of $16.50

and then an additional 3

cents per minute of use. For what amounts of monthly phone use will Plan A cost at least as much as Plan B?

Use m

for the number of minutes of phone use in a month, and solve your inequality for m

.

Answer 1

This question is looking for an intersection point of two lines. One line is an equation for Plan A and the other is an equation for Plan B. So let's try to find the equation for Plan A. We can use the formula y=mx+b and fill in what we know to create an equation for this line. The plan states that a customer pays 6 cents ($.06) for every minute they spend on the phone. So we know that every minute costs 6 cents, but we don't know how many minutes they use. The equation becomes y=.06x+0.

Let's break that equation down. X represents every minute spent on the phone and we know that every minute costs $.06 or 6 cents. Since there is no monthly fee, the only thing they pay for is the time they use, this is where we get the 0 from in our equation. Y would be our answer if we plugged anything in for x.

Now for Plan B, we can again use the formula y=mx+b but this time we do have a monthly fee of $16.50. This means regardless of how many minutes they use, they must pay $16.50, no matter what. However, they also get charged $.03 (3 cents) every minute they spend on their phone. So our equation becomes y=.03x+16.50

Lets break that equation down as well. For every minute spent on the phone they must pay $.03 and since we don't know how many minutes they use, we keep that as a variable. (X in this case). However, if they do not use any minutes, they still have to pay $16.50.

Now since we want to find what amounts of monthly phone use will Plan A cost at least as much as Plan B, we need to solve for the amount of phone usage. You'll notice both equations have a "y" isolated on one side of the equation. We can use this to set the equations equal to each other by replacing the y of one equation with the right side of the other equation. So we have y=.06x and y=.03x+16.50. We can turn these into one equation which becomes .06x=.03x+16.50.

In order to find when the plans' cost will be at least the same, we need to solve for x. If we subtract .03x from both sides we are left with

.03x=16.50. Now all we need to do is divide both sides by .03 and we will have the spot where the lines intersect.

x=550. This means that in either plan A or B, 550 minutes of use will cost the same. We can check this by plugging 550 in for x in both equations.

.06(550)=$33

.03(550)+16.50=$33

Hope this helps!

Answer 2

Plan A costs 6 cents per minute (A = 0.06m)

Plan B has a flat rate of $16.50 plus 3 cents per minute (B = 16.5 + 0.03)

When is A at least as much as B (A ≥ B)?

Solve this inequality:

0.06m ≥ 16.5 + 0.03m (subtract 0.03m from both sides in order to get the variables on one side)

0.03m ≥ 16.5 (divide both sides by 0.03 in order to get the variable by itself)

m ≥ 550

Plan A will cost at least as much as Plan B at 550 minutes.