Problem A and Solution

Deciding About Data

The Webb family is trying to decide on a new monthly internet plan. There are three choices:

Plan A: \(\$10\) for the first \(10\) GB of data, and each additional \(2\) GB costs \(\$5\).

Plan B: \(\$40\) for the first \(20\) GB of data, and each additional \(10\) GB costs \(\$10\).

Plan C: \(\$80\) for unlimited GB of data.

Note that for Plan A, additional data has to be purchased in \(2\) GB increments. Similarly, for Plan B, additional data has to be purchased in \(10\) GB increments.

After keeping track of data used, the family decides they will use between \(25\) GB and \(40\) GB of data each month. Which plan should the Webb family choose? Justify your answer.

One way to make a decision is to make a table showing how much each plan would cost for various amounts of data use.

Data Used (in GB) |
Total Cost (in $) for Plan A |
Total Cost (in $) for Plan B |
Total Cost (in $) for Plan C |
---|---|---|---|

\(10\) | \(10\) | \(40\) | \(80\) |

\(12\) | \(15\) | \(40\) | \(80\) |

\(14\) | \(20\) | \(40\) | \(80\) |

\(16\) | \(25\) | \(40\) | \(80\) |

\(18\) | \(30\) | \(40\) | \(80\) |

\(20\) | \(35\) | \(40\) | \(80\) |

\(22\) | \(40\) | \(50\) | \(80\) |

\(24\) | \(45\) | \(50\) | \(80\) |

\(26\) | \(50\) | \(50\) | \(80\) |

\(28\) | \(55\) | \(50\) | \(80\) |

\(30\) | \(60\) | \(50\) | \(80\) |

\(32\) | \(65\) | \(60\) | \(80\) |

\(34\) | \(70\) | \(60\) | \(80\) |

\(36\) | \(75\) | \(60\) | \(80\) |

\(38\) | \(80\) | \(60\) | \(80\) |

\(40\) | \(85\) | \(60\) | \(80\) |

Notice that at \(25\) GB, with Plan A they would need to get \(26\) GB of data. This would cost \(\$50\). So, comparing the cost of the plans, we notice that Plan B is the lowest price from \(25\) GB to \(40\) GB. Therefore, the family should choose Plan B.

(Note that if the family uses less than \(25\) GB per month, then Plan A is better. Also, if they use more than \(40\) GB, then it looks like Plan B is better at first, but Plan C will eventually be better.)