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Teresa wants to buy a new cell phone. She wants to get a phone with a good text message plan. She is deciding between Verizon and AT&T. Verizon charges a monthly fee of $25 and $0.05 per text message. AT&T charges a monthly fee of $15 and $0.10 per text message. After how many text messages will the costs be the same? Which company should she choose if she sends 100 text messages per month?

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sqdancefan

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Answer:

  • 200 messages
  • Verizon

Step-by-step explanation:

The cost of the AT&T plan for m messages is ...

  a(m) = 25 +0.05m

The cost of the Verizon plan for m messages is ...

  v(m) = 15 +0.10m

The two plans have equal costs when ...

  a(m) = v(m)

  25 + 0.05m = 15 + 0.10m

  10 = 0.05m . . . . . . . . . . . . . . subtract 15+0.05 m from both sides

  200 = m . . . . . . . . . multiply both sides by 20

The plans have the same cost for 200 messages.

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For fewer than 200 messages, the plan with the lower fixed fee is the better choice.

Teresa should choose the Verizon plan.

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