Final answer:
Both Plan A and Plan B will cost the same amount after 1700 minutes of use. This is determined by setting up and solving an equation where both plans' costs are equal when accounting for the base fee and per-minute charge after the allotted free minutes.
Step-by-step explanation:
To find out after how many minutes both Plan A and Plan B would cost the same amount, we need to set up an equation that equals the total costs of both plans and then solve for the number of minutes. Let's denote the number of minutes as m.
For Plan A, since the first 500 minutes are free, we only start paying after 500 minutes. The cost will be:
Cost of Plan A = $50 + ($0.05 × (m - 500) )
For Plan B, the first 200 minutes are free, so the cost will be:
Cost of Plan B = $20 + ($0.06 × (m - 200) )
We want the costs to be equal, so we set the two equations to each other:
$50 + $0.05(m - 500) = $20 + $0.06(m - 200)
Now, solve for m:
- Expand both equations:
$50 + $0.05m - $25 = $20 + $0.06m - $12 - Simplify:
$25 + $0.05m = $8 + $0.06m - Rearrange the equation to get all terms involving m on one side and constants on the other:
$0.05m - $0.06m = $8 - $25 - Simplify:
-$0.01m = -$17 - Divide by -0.01 to solve for m:
m = $17 / $0.01 - Calculate m:
m = 1700 minutes
This means both plans will cost the same amount after 1700 minutes.