# Grid-Ins

## Student-Produced Response

RESULTS OF AN ELECTION | |

Candidate | Number of Votes |
---|---|

X | 7,400 |

Y | 2,375 |

Z | 5,250 |

The results for three candidates in an election are shown in the table above. If each voter voted for exactly one candidate, what is the fewest number of voters who would have had to vote differently in order for Candidate *Z* to have received more votes than Candidate *X*?

Correct Answer: 1076

**Explanation:**

For this question, let *k* be the number of voters who changed their vote. Since you want to make *k* as small as possible, the *k* voters should come from those who voted for Candidate *X.* To determine an answer to the problem, you would need to solve the inequality 5,250 + *k* > 7,400 - *k*. Solving this inequality yields 2*k* > 2150 or *k* > 1075. Therefore, 1,076 voters who had voted for Candidate *X* would have to change their vote and vote for Candidate *Z* in order for Candidate *Z* to receive more votes than Candidate *X.* The correct answer to this question is 1076.

(from the October 16, 1999 test)