Question

Customers of a phone company can choose between two service plans for long distance calls. The first plan has no monthly fee but charges
$
0.17

for each minute of calls. The second plan has an
$
18

monthly fee and charges an additional
$
0.12

for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 1

Hi there! So we are talking about the first plan being 17¢ per minute, but with no monthly fee. The other place has a fixed monthly fee of $18, but charges 12¢ per minute. To solve for the amount of minutes it would take for both plan to be equal, we can write and solve an equation. Set it up like this:

0.17m = 18 + 0.12m

This is because we are talking about $0.17 per minute for the first plan, and the second plan $0.12 per minute, with the fixed, one-time price of $18. The variable m stands for minutes. The amount goes up the more minutes you talk on the phone. First off, let's subtract 0.12m from both sides. 0.12m - 0.12m cancel each other out. 0.17m - 0.12m = 0.05m. The equation simplified is 0.05m = 18. Divide each side by 0.05 to isolate the m. 0.05m/0.05 cancel each other out. 18/0.05 is 360. We have a possible value of m. Let's substitute that number for m and see if it works. 360 * 0.17 is 61.2. 360 * 0.12 is 43.2. 43.2 + 18 is 61.2. 61.2 = 61.2. There. m = 360. It would take 360 minutes of calls for both plans to be equal.

Answer 2

0.17x = 0.12x +18

subtract 0.12x from each side

0.05x = 18

divide both sides by 0.05

x = 18/0.05 = 360

 360 minutes would be the answer

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