Question

One cable company charges $50 per month for their basic plan, plus $75

installation. A second company charges $55 per month, but offers free
installation. For what number of months is the first plan cheaper than the
second plan?
Write your answer as a number, with no symbols, spaces, or words.
Your answer

Answer 1

To find out for how many months the first plan is cheaper, an equation based on the monthly fee and installation cost is set up and solved, revealing that the first plan is cheaper for 15 months.

Step-by-step explanation:

We need to calculate the number of months for which the first cable plan is less expensive than the second. The first plan costs $50 per month plus a one-time $75 installation fee. The second plan costs $55 per month with no installation fee. To compare the two, we set up an equation where the total cost of the first plan is equal to the total cost of the second plan:

50m + 75 = 55m

where m represents the number of months. By subtracting 50m from both sides, we get:

75 = 5m

Divide both sides by 5:

m = 15

Thus, the first plan is cheaper for 15 months.

Answer 2

Step-by-step explanation:

One cable company charges $50 per month for their basic plan, plus $75 installation. A second company charges $55 per month, but offers free installation. For what number of months is the first plan cheaper than the second plan?

50m + 75 < 55m

subtract 50m from both sides:

50m + 75 -50m < 55m - 50m

75 < 5m

divide both sides by 5:

75/5 < 5m/5

15 < m

or m > 15

so:

The first plan cheaper than the second plan after 16+ months