The equation \(3x = 24\) can be interpreted in the context of the scenarios provided.
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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?
- Here, \(x\) would represent the total number of surveyed students. Since one-third of the total equals 24, this can be represented as \(x/3 = 24\), or rearranged to \(x = 3 \times 24\), which is \(3x = 24\).
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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?
- For this scenario, if the shirt costs $24, then the equation would be \(3x = 24\), where \(x\) is the cost of the shirt, which is incorrect because the right equation would be \(x = 24\) and shoes would then cost \(3 \times 24\).
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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, let \(x\) be the number of weeks. Since he lists 3 words each week, it would be \(3x = 24\). This fits perfectly with 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, each of the three people received 24 stickers, meaning the total number of stickers is \(3 \times 24\), which would be \(x = 3 \times 24\), which doesn't represent \(3x = 24\).
Therefore, the correct interpretation of the equation \(3x = 24\) is given by:
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?