Comparing phone service plans using linear equations

¶ … Algebra

Many times when purchasing a service there are choices to make. This man is totally confused and frustrated about his options.

One example is phone service:

A telephone company has a choice of two plans. Plan A - $30 per month and $.05 per phone call and Plan B - $20 per month and $.10 per phone call. Which is the best plan for you?

By the end of this discussion, you will have demonstrated your ability to:

Explain two possible plans that provide the same service

The first plan is saying that there is a fixed cost at $30 per month and then there is a variable cost associated with it which is $0.05 cents per phone call- this is a variable cost because it is dependent on how many phone calls are actually made. The second plan is saying there is a fixed cost of $20 per month and then the variable cost associated with this is $0.10 per call- this is a variable cost and is directly dependent on how many calls are actually made by the user.

Create two equations in two variable based on two options

Option for Plan A:

$30 + (0.05x)

Option for Plan B:

$20 + (0.10x)

Determine the best option given two plans

Step 1: $30 + (0.05x) = $20 + (0.10x)

Step 2: Subtract (0.05x) from both sides-

$30 + (0.05x) -- (0.05x) = $20 +(0.10x) -- (0.05x) ? $30 = $20 + (0.05x)

Step 3: Subtract $20 from each side-

$30 - $20 = $20 -$20 + (0.05x) ? $10 = (0.05x)

Step 4: Divide both sides by (0.05) to isolate x:

$10 / (0.05) = (0.05x)/(0.05)

200 = x

After making 200 phone calls, both plans will break even so it doesn't matter which plan you are choosing if you are making 200 phone calls.

If you plan on making less than 200 phone calls, then one should assign a random value to x less than 200:

$30 + (0.05 x 100)= $35

$20 + (0.05 x 100) = $25