Solving a decimal word problem using a linear equation with the variable on both sides

Question

Problem Page
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a
$29
monthly fee and charges an additional
$0.09
for each minute of calls. The second plan has a
$13
monthly fee and charges an additional
$0.13
for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 1

Note that all calculations are "per month."

 

The cost per month equals (monthly fee) + (cost per minute)*(number of minutes).

 

Let x = number of minutes

 

First Plan:   $29 + $0.09x                   

 

Second Plan:    $13 + $0.13x

 

The plans are equal when:

    $29 + $0.09x = $13 + #0.13x

 

    2900 + 9x = 1300 + 13x             [multiply by 100 to get rid of decimals]

     1600 = 4x                              [subtract 1300, subtract 9x on both sides]

        400 = x

 

The monthly costs are equal when 400 minutes are used.

 

Check:

  Is      $29.00 + $0.09(400) = $13.00 + $0.13(400)   ?

           $29.00 + $36.00 = #13.00 + $52.00   ?

                 $65.00 = $65.00   ?yes

Answer 2

This is a system of equations question. 

You will need two equations.

 

Equation 1 is: y=29+.09x

Equation 2 is very similar.

 

After you have both of your equations. You need then solve the system by either substitution or elimination. This will tell you their intersection point/when the plans will be equal for a particular amount of minutes.