The equation \(3x = 24\) can be solved for \(x\) by dividing both sides by 3:
\[ x = \frac{24}{3} = 8 \]
This means that \(x\) equals 8.
Now let's look at the options provided to determine which scenario corresponds to the equation:
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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?
- This scenario can be represented by the equation \(3x = 24\). Here, \(x\) represents the number of weeks, and since Andrew picks 3 words each week, \(3x\) equals the total number of words listed (24).
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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?
- This situation is not represented by \(3x = 24\) because it would be represented by \(x = 24\) (the cost of the shirt) and then multiplying by 3 for the shoes.
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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?
- This situation would be represented by \(3x = y\), where \(y\) is the total number of stickers, not directly fitting 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?
- This would be represented by \( \frac{1}{3}x = 24\), so it does not fit \(3x = 24\).
Therefore, the scenario that can be represented by the equation \(3x = 24\) is the first one regarding Andrew and his words.
Answer: 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?