Question

The Pirouette Dance Team needs more than $300 to cover costume expenses. They have $75 and plan to sell raffle tickets, r, for $5 each in order to raise money.
Which statement is true about the solution for the inequality that represents this situation?
Responses
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.


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.


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.




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.

Answer 1

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.

1. Let \( r \) be the number of raffle tickets sold. Since each ticket is $5, the money raised from selling \( r \) tickets would be \( 5r \).
2. The total amount of money they would have after selling \( r \) tickets is \( 5r + 75 \).
3. They need this amount to be greater than $300. This leads us to the inequality:

\[
5r + 75 > 300
\]

4. 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:

1. **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.)

2. **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.)

3. **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.)

4. **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.**