Question

A popular cell phone family plan provides 1500 minutes. It charges 89.99/month for the first 2 lines and 9.99 for every line after that. Unlimited text messages for all phone lines costs $30.00/month, and Internet costs $10.00/month per phone line. If a family with a $200 monthly budget buys this plan and signs up for unlimited text messaging and Internet on each phone line, how many cell phone lines can they afford? Use an inequality to solve this problem. Graph your solution on the number line and explain the meaning of your graph in a sentence.

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Seamus

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To solve this problem, let's first set up an inequality to represent the situation.

Let x be the number of cell phone lines the family can afford.

The monthly cost for the first 2 lines is $89.99 each, so the total cost for these lines is $89.99 + $89.99 = $179.98.

For each additional line after the first 2, the cost is $9.99. Since there are x - 2 additional lines after the first 2, the cost for these lines is 9.99 * (x - 2).

In addition, the family has to pay $30.00/month for unlimited text messages for all phone lines and $10.00/month for Internet per phone line.

So the total monthly cost, including the text messages and Internet, can be expressed as:

179.98 + 9.99 * (x - 2) + 30.00 + 10.00x ≤ 200.00

Simplifying the inequality, we have:

179.98 + 9.99x - 19.98 + 30 + 10.00x ≤ 200.00

-9.99x + 9.99x + 19.99x ≤ 200.00 - 179.98 - 30 - 19.99

39.98x ≤ 190.03

Now, we can solve for x:

x ≤ \dfrac{190.03}{39.98}

x ≤ 4.7529

Since we cannot have a fractional number of cell phone lines, the family can afford a maximum of 4 lines.

Answer: The family can afford a maximum of 4 cell phone lines.

Let x be the number of cell phone lines the family can afford.

The monthly cost for the first 2 lines is $89.99 each, so the total cost for these lines is $89.99 + $89.99 = $179.98.

For each additional line after the first 2, the cost is $9.99. Since there are x - 2 additional lines after the first 2, the cost for these lines is 9.99 * (x - 2).

In addition, the family has to pay $30.00/month for unlimited text messages for all phone lines and $10.00/month for Internet per phone line.

So the total monthly cost, including the text messages and Internet, can be expressed as:

179.98 + 9.99 * (x - 2) + 30.00 + 10.00x ≤ 200.00

Simplifying the inequality, we have:

179.98 + 9.99x - 19.98 + 30 + 10.00x ≤ 200.00

-9.99x + 9.99x + 19.99x ≤ 200.00 - 179.98 - 30 - 19.99

39.98x ≤ 190.03

Now, we can solve for x:

x ≤ \dfrac{190.03}{39.98}

x ≤ 4.7529

Since we cannot have a fractional number of cell phone lines, the family can afford a maximum of 4 lines.

Answer: The family can afford a maximum of 4 cell phone lines.

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