To determine which of the scenarios can be represented by the equation \(3x = 24\), let's analyze each option:
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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?
- In this case, \(x\) would represent the number of weeks, and each week he picks 3 words, leading to \(3x = 24\). This matches the 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?
- Here, if \(x\) was the total number of stickers, it would be represented by \(x/3 = 24\), leading to \(x = 72\). This does not match \(3x = 24\).
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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 case, if \(x\) is the total number of students surveyed, then \(\frac{x}{3} = 24\), leading to \(x = 72\). This does not match \(3x = 24\).
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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?
- Since the cost of the shoes is three times the cost of the shirt, it would be represented as \(3 \times 24 = 72\). That leads to an expression of the form \(y = 3(24)\), but it is not set up as \(3x = 24\).
The only scenario that matches the equation \(3x = 24\) is the first one about Andrew, where he picks three words a week, and the total is 24 words.
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?