To determine which of the scenarios can be represented by the equation \( 3x = 24 \), we can solve for \( x \):
\[ x = \frac{24}{3} = 8 \]
Now, we will evaluate each statement:
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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 \( x \) is the number of weeks, then the total number of words listed is given by \( 3x = 24 \). This matches our equation. So, Andrew has been doing this for \( 8 \) weeks.
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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 surveyed students, then \( \frac{1}{3}x = 24 \) or \( x = 72 \). This does not match our 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?
- Here, if \( x \) is the cost of a shirt ($24), then the equation would be \( 3 \times 24 = 72 \) for the pair of shoes. This does not match our 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 case, if there are 3 people and each received 24 stickers, the total is \( 3x = 24 \). Here, \( x = 8 \) (total stickers divided by 3 people). Therefore, Rita bought \( 72 \) stickers. This does match the same structure but does not solve for \( x \).
Overall, the scenario that directly corresponds to the equation \( 3x = 24 \) is:
- Andrew's scenario: He has been doing this for \( 8 \) weeks.
Thus, the answer is that the equation \( 3x = 24 \) can be represented by Andrew's scenario.
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