Problem A and Solution

Holiday Cheer

Students at Giving Elementary School are spreading holiday cheer this year by collecting donations for families in need within their community. Their goal this year was to collect \(2000\) items in one week, and they exceeded their goal! The table below shows the number of donations each day during the week.

Day | Number of Items Donated |
---|---|

Monday | \(392\) |

Tuesday | \(46\) |

Wednesday | \(877\) |

Thursday | ? |

Friday | \(229\) |

Someone accidentally tore the collection sheet with the data on it, so they don’t have the number of items they collected on Thursday. If we know the school exceeded their goal of \(2000\) items in a week, what is the minimum number of items the students collected on Thursday?

We start by adding up the number of items for the days we know, and we get \(392 + 46 + 877 + 229 = 1544.\)

Since we know the students exceeded their goal, then they must have collected at least \(2001\) items in total. Thus, the minimum number of items they collected on Thursday must be \(2001 - 1544 = 457.\)