To solve the equation \(3x = 24\) for \(x\), we divide both sides by 3:
\[ x = \frac{24}{3} = 8 \]
Now, let's analyze each of the options to see which can be represented by this equation:
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Andrew's situation: 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?
- In this case, \(x\) represents the number of weeks, and since he picks 3 words each week, \(3 \times x = 24\). This fits the equation.
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Rita's situation: Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?
- Here, each of the three people receives 24 stickers, so \(3x = 24\) would imply \(x\) is the number of stickers each person gets, which is not what the equation represents.
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Shoes and shirt cost: 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 situation, if the shirt costs 24, we calculate the shoes as \(3 \times 24\), so it does not fit the equation \(3x = 24\) for any variable \(x\).
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Survey result: 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?
- Here, this does not directly fit \(3x = 24\) and is instead a different kind of equation relating to fractions.
Thus, the correct response 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?