Problem A and Solution

Better Deal?

From a candy machine, I can buy \(8\) candies for \(25\) cents. Alternatively, I can buy \(64\) candies in a package for \(2\) dollars and \(20\) cents.

If I want to buy 128 candies for my class, how should I buy the candies in order to spend the least amount of money?

Note: \(1\) dollar is equal to \(100\) cents.

Since \(128\) is equal to \(2 \times 64\), two packages of candies will be enough for the class. This would cost \(2 \times \$2\) plus \(2 \times 20\) cents, for a total of \(\$4\) and \(40\) cents.

We can use skip counting to calculate how much the candies will cost if we buy them from the candy machine. This is summarized in the table below.

Number of Candies |
Cost (cents) |
---|---|

\(8\) | \(25\) |

\(16\) | \(50\) |

\(24\) | \(75\) |

\(32\) | \(100\) |

\(40\) | \(125\) |

\(48\) | \(150\) |

\(56\) | \(175\) |

\(64\) | \(200\) |

Thus, \(64\) candies from the candy machine will cost \(200\) cents, which is equal to \(\$2\). This is less than the cost of \(64\) candies in a package.

Therefore, to spend the least amount of money, we should buy all \(128\) candies from the candy machine. The total cost will then be \(2\times \$2 = \$4\).