Question
If the associated student body decides to host this dance, their goal is to have a total of 261 students attend. If the seventh-grade class and the eighth-grade class exactly meet their goals for attendance, what percent of sixth-grade students would need to attend for the club to meet its goals? Explain or show your reasoning. You may use a combination of diagrams, drawings, expressions/equations, and words.
Answers
GPT-4o mini
To determine the percentage of sixth-grade students that need to attend the dance, we first let’s denote the number of students from each grade that are expected to attend.
Let:
- \( x \) be the number of sixth-grade students that attend.
- The number of seventh-grade students expected to attend is given as \( S \).
- The number of eighth-grade students expected to attend is given as \( E \).
According to the problem, we have the following total attendance goal:
\[
x + S + E = 261
\]
Next, we assume that the seventh and eighth grades have their attendance goals met. If we know \( S \) and \( E \), we can express these values. Let’s say, for example:
- The seventh grade has a goal of \( S \) students.
- The eighth grade has a goal of \( E \) students.
We don’t have their specific attendance goals, so let's just designate them as numbers. For the sake of calculations, let’s assume hypothetical values for \( S \) and \( E \). Suppose:
- \( S = 100 \)
- \( E = 80 \)
Now substituting these values into our total attendance equation gives:
\[
x + 100 + 80 = 261
\]
This simplifies to:
\[
x + 180 = 261
\]
Next, we solve for \( x \):
\[
x = 261 - 180
\]
\[
x = 81
\]
This means that 81 sixth-grade students must attend the dance to meet the goal.
Now, to find out what percent \( y \) of the sixth-grade class needs to attend, we need to know the total number of sixth-grade students. Let’s denote the total number of sixth-grade students as \( T \).
To find the percentage of sixth-graders who need to attend, we use the formula for percentage:
\[
\text{Percentage} = \left( \frac{\text{Number of sixth-grade students attending}}{\text{Total sixth-grade students}} \right) \times 100
\]
This gives us:
\[
y = \left( \frac{81}{T} \right) \times 100
\]
Since we don’t have a concrete number for \( T \), we can't calculate an exact percentage. However, if we assume \( T \) is known, you can plug in that value into the equation to find the specific percentage required.
For example:
- If there are 150 sixth-grade students total, the calculation would be:
\[
y = \left( \frac{81}{150} \right) \times 100 \approx 54\%
\]
In conclusion, once the value of \( T \) is clear, we can find out the percentage of sixth-grade students needed to attend to help meet the target attendance of 261 students. If you have specific numbers for seventh and eighth grades or for total sixth graders, you can adjust the calculations accordingly.
Let:
- \( x \) be the number of sixth-grade students that attend.
- The number of seventh-grade students expected to attend is given as \( S \).
- The number of eighth-grade students expected to attend is given as \( E \).
According to the problem, we have the following total attendance goal:
\[
x + S + E = 261
\]
Next, we assume that the seventh and eighth grades have their attendance goals met. If we know \( S \) and \( E \), we can express these values. Let’s say, for example:
- The seventh grade has a goal of \( S \) students.
- The eighth grade has a goal of \( E \) students.
We don’t have their specific attendance goals, so let's just designate them as numbers. For the sake of calculations, let’s assume hypothetical values for \( S \) and \( E \). Suppose:
- \( S = 100 \)
- \( E = 80 \)
Now substituting these values into our total attendance equation gives:
\[
x + 100 + 80 = 261
\]
This simplifies to:
\[
x + 180 = 261
\]
Next, we solve for \( x \):
\[
x = 261 - 180
\]
\[
x = 81
\]
This means that 81 sixth-grade students must attend the dance to meet the goal.
Now, to find out what percent \( y \) of the sixth-grade class needs to attend, we need to know the total number of sixth-grade students. Let’s denote the total number of sixth-grade students as \( T \).
To find the percentage of sixth-graders who need to attend, we use the formula for percentage:
\[
\text{Percentage} = \left( \frac{\text{Number of sixth-grade students attending}}{\text{Total sixth-grade students}} \right) \times 100
\]
This gives us:
\[
y = \left( \frac{81}{T} \right) \times 100
\]
Since we don’t have a concrete number for \( T \), we can't calculate an exact percentage. However, if we assume \( T \) is known, you can plug in that value into the equation to find the specific percentage required.
For example:
- If there are 150 sixth-grade students total, the calculation would be:
\[
y = \left( \frac{81}{150} \right) \times 100 \approx 54\%
\]
In conclusion, once the value of \( T \) is clear, we can find out the percentage of sixth-grade students needed to attend to help meet the target attendance of 261 students. If you have specific numbers for seventh and eighth grades or for total sixth graders, you can adjust the calculations accordingly.