For how many minutes of calls will the costs of the two plans be equal?

Question

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a
$16
monthly fee and charges an additional
$0.15
for each minute of calls. The second plan has no monthly fee but charges
$0.19
for each minute of calls.

Answer 1

Let's solve this problem using algebra. Set M equal to the monthly fee for the first plan, X equal to the cost of an additional minute of calls for the first plan, Y equal to the cost of an additional minute of calls for the second plan, and N equal to the total number of minutes called.

 

Our algebra equation, stated in words, is this: "the cost of the monthly fee for the first plan PLUS the cost-per-call-per-minute for the first plan TIMES the number of call minutes IS EQUAL TO the cost-per-call-per-minute for the second plan TIMES the number of call minutes". Restated in terms of an algebra equation...

 

M + XN = YN

 

Now, let's solve this equation:

• M + XN = YN (original equation)
• 16 + 0.15N = 0.19N (plugging in the values from the word problem)
• 16 + 0.15N - 0.15N = 0.19N - 0.15N (subtracting 0.15N from both sides)
• 16 = 0.19N - 0.15N (subtracting the N terms on the left side)
• 16 = 0.04N (subtracting the N terms on the right side)
• 16/0.04 = 0.04N/0.04 (dividing both sides by 0.04)
• 400 = 0.04N/0.04 (simplifying the left side)
• 400 = N (simplifying the right side)

 

Thus, if 400 minutes of calls are made, the costs of both plans will be equal.