To analyze this situation, we start by setting up the inequality based on the information given. The Pirouette Dance Team currently has $75 and they need to raise more than $300 via selling raffle tickets at $5 each.
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Let \( r \) be the number of raffle tickets sold. Since each ticket is $5, the money raised from selling \( r \) tickets would be \( 5r \).
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The total amount of money they would have after selling \( r \) tickets is \( 5r + 75 \).
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They need this amount to be greater than $300. This leads us to the inequality:
\[ 5r + 75 > 300 \]
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Now, we solve the inequality:
\[ 5r > 300 - 75 \] \[ 5r > 225 \] \[ r > 45 \]
The solution \( r > 45 \) indicates that they need to sell more than 45 tickets. Thus, the minimum number of tickets that need to be sold to raise more than $300 is 46.
Now let's evaluate the choices provided:
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5r + 75 > 300 represents this situation, and the solution r > 45 means that it will take a minimum of 46 tickets to raise the needed money. (This statement is true.)
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5r + 75 > 300 represents this situation, and the solution r > 45 means that it will take a minimum of 45 tickets to raise the needed money. (This statement is false; it should be 46 tickets.)
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5r + 75 ≥ 300 represents this situation, and the solution r ≥ 45 means that it will take a maximum of 45 tickets to raise the needed money. (This statement is false; the inequality is greater than, not greater than or equal to, and it does not imply a maximum.)
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5r + 75 ≥ 300 represents this situation, and the solution r ≥ 45 means that it will take a minimum of 46 tickets to raise the needed money. (This statement is false because the inequality should be >, not ≥.)
Therefore, the correct statement is:
5r + 75 > 300 represents this situation, and the solution r > 45 means that it will take a minimum of 46 tickets to raise the needed money.