The equation \(3x = 24\) can be interpreted in relation to the scenarios given. Here’s how it applies to each option:
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Favorite Subject Survey: "One-third of all surveyed, or 24 students, said math is their favorite subject." This means if \(x\) is the total number of students surveyed, then \(\frac{x}{3} = 24\) which leads to \(x = 3 \times 24 = 72\). This scenario does not fit \(3x = 24\).
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Andrew's Words: "Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words." The total number of words listed can be represented by \(3x = 24\) where \(x\) is the number of weeks Andrew has been doing this. Therefore, \(x = \frac{24}{3} = 8\). This scenario fits \(3x = 24\).
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Rita's Stickers: "Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers." If there are 3 people and each received 24 stickers, the total number of stickers purchased by Rita would be \(3 \times 24 = 72\), which does not fit \(3x = 24\).
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Cost of Shoes: "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?" The shoes cost is \(3 \times 24 = 72\), which does not fit \(3x = 24\).
Out of all the options, the scenario involving Andrew fits the equation \(3x = 24\), where \(x\) represents the number of weeks Andrew has been listing words.
So, the correct answer 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?