Answer:
1) Six months
2) The second plan ($30 sign up fee, $5 per month)
Explanation:
1) Six months
We can write an equation such as 30 + 5m = x, where m = months and x = total cost after a certain amount of months. If we know that the first plan costs $12 a month, we can find the LCM of 12 and 30 + 5m, which is 60. If we plug in 60 as m in the equation I showed, we'll get this:
30 + 5m = 60
Solve for x = 6.
2) The second plan
Write the first plan as an equation 12m = x, where m is months and x is the total cost after a certain amount of months. If we plug in 12 for m (since there's 12 months in a year), we'll get 12(12) = x, where x is equal to $144 after a year.
Write the second plan as an equation 30 + 5m = x, where m is months and x is the total cost after m months. Plug in 12 again so our equation looks like
30 + 5(12) = x. Solve for x and get $90 after a year.