To solve the equation \(3x = 24\), we can divide both sides by 3:
\[ x = \frac{24}{3} = 8 \]
Now, let's analyze the provided responses to see which situation fits this equation:
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Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?
- In this scenario, there are 3 people (Rita + 2 friends), so the total number of stickers would be \(3 \times 24 = 72\). This does not fit the equation \(3x = 24\) because we would need \(x = 72 \div 3 = 24\).
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Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?
- Here, if Andrew picks 3 words each week, we can set up the equation \(3x = 24\) where \(x\) is the number of weeks. Solving gives \(x = 8\). This fits the equation.
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The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?
- In this case, the cost of the shoes would be \(3 \times 24 = 72\), which does not relate directly to the equation \(3x = 24\).
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A survey was conducted to determine the favorite subject of seventh grade students. One-third of all surveyed, or 24 students, said math is their favorite subject. How many students were surveyed?
- In this scenario, if \(x\) is the total number of students surveyed, we have \(\frac{1}{3}x = 24\). This simplifies to \(x = 24 \times 3 = 72\), which also does not fit the equation \(3x = 24\).
The only situation that can be represented by the equation \(3x = 24\) is:
Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?