Jenna is deciding between two cell-phone plans. The first plan has a $50 sign-up fee and costs $20 per month. The second plan has a $30 sign-up fee and costs $25 per month. After how many months will the total costs be the same?
For the first plan, the total cost after m months will be: 50 + (20 * m).
For the second plan, the total cost after m months will be: 30 + (25 * m).
We want to find the value of m for which the total costs are the same, so we can set the two expressions equal to each other and solve for m:
50 + (20 * m) = 30 + (25 * m)
Subtract 30 from both sides:
20 * m = 20 + (25 * m)
Subtract 20 * m from both sides:
0 = 20 + (5 * m)
Subtract 20 from both sides:
-20 = 5 * m
Divide both sides by 5:
-4 = m
Therefore, the total costs will be the same after 4 months.