Help Please.
A wireless phone company offers two plans. In one plan, there is a monthly fee of $40 and a charge of $0.25 per minute. In the other plan, there is monthly fee of $25 and a charge of $0.40 per minute. For what number of minutes are the costs equal?
To find the number of minutes where the costs for both plans are equal, we need to set up an equation where the total cost for both plans is the same. Let's call the number of minutes "m".
For the first plan, the total cost is the monthly fee of $40 added to the cost per minute ($0.25) multiplied by the number of minutes:
Cost of Plan 1 = $40 + ($0.25 * m)
For the second plan, the total cost is the monthly fee of $25 added to the cost per minute ($0.40) multiplied by the number of minutes:
Cost of Plan 2 = $25 + ($0.40 * m)
Now, we set these two equations equal to each other to find the number of minutes where the costs are equal:
$40 + ($0.25 * m) = $25 + ($0.40 * m)
To solve for "m", we can simplify the equation:
$40 - $25 = ($0.40 * m) - ($0.25 * m)
$15 = $0.15 * m
Now, let's solve for "m" by dividing both sides of the equation by $0.15:
m = $15 / $0.15
m = 100
Therefore, the costs for both plans are equal at 100 minutes.
In order, these equations are:
1) .25x + 40
2) .40x + 25
Where the charge per minute is the slope, the flat rate the y-intercept.
We want to know for what number of minutes these two plans cost the same, so set equations (1) and (2) equal to each other and solve for x.