Problem A and Solution

Saving Up

Fionnlay earns \(\$8\) each week by walking the neighbour’s dog. Starting in the second week, Fionnlay earns an extra \(\$3\) by helping maintain the community garden every other week. He is saving all of his earnings for a bicycle, which costs \(\$157\). He will also need a helmet which costs \(\$24\), a bike horn which costs \(\$16\), and a bike light which costs \(\$9\). All prices include taxes. Fionnlay keeps track of the money he has earned.

How much money will Fionnlay have saved after \(8\) weeks?

How much money will Fionnlay have saved after \(15\) weeks?

How long will it take him to save enough money to buy the bike and its accessories?

One way to solve this problem is to create a table that records the total that Fionnlay has saved each week. In the odd-numbered weeks, the total will increase by \(\$8\). In the even-numbered weeks, the total will increase by \(\$8 + \$3 = \$11\).

We will also need to know how much money Fionnlay needs to save by calculating the total cost of the bike and its accessories. We can do this by adding \(\$157 + \$24 + \$16 + \$9 = \$206\).

Week |
Increase (in $) |
Total Savings (in
$) |
---|---|---|

\(1\) | \(8\) | \(8\) |

\(2\) | \(11\) | \(19\) |

\(3\) | \(8\) | \(27\) |

\(4\) | \(11\) | \(38\) |

\(5\) | \(8\) | \(46\) |

\(6\) | \(11\) | \(57\) |

\(7\) | \(8\) | \(65\) |

\(8\) | \(11\) | \(76\) |

\(9\) | \(8\) | \(84\) |

\(10\) | \(11\) | \(95\) |

\(11\) | \(8\) | \(103\) |

\(12\) | \(11\) | \(114\) |

\(13\) | \(8\) | \(122\) |

\(14\) | \(11\) | \(133\) |

\(15\) | \(8\) | \(141\) |

\(16\) | \(11\) | \(152\) |

\(17\) | \(8\) | \(160\) |

\(18\) | \(11\) | \(171\) |

\(19\) | \(8\) | \(179\) |

\(20\) | \(11\) | \(190\) |

\(21\) | \(8\) | \(198\) |

\(22\) | \(11\) | \(209\) |

Using the table, we can now answer the questions.

Fionnlay will have saved \(\$76\) after \(8\) weeks.

Fionnlay will have saved \(\$141\) after \(15\) weeks.

Fionnlay will need \(22\) weeks to save enough money for the bike and its accessories.