To determine which scenario can be represented by the equation \(3x = 24\), we need to interpret what the equation is saying. In this equation, \(x\) is a variable that represents a quantity, and \(3x\) suggests that whatever quantity \(x\) represents is multiplied by 3.
Now, let's analyze each response:
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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 does not fit the equation \(3x = 24\) since \(x\) would represent the cost of the shoes. The shoes would be \(x = \frac{24}{3} = 8\), not fitting the scenario.
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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 \(\frac{1}{3} \cdot x = 24\), which does not match \(3x = 24\).
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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?
- This scenario would be expressed as \(3x = 24\), where \(x\) would equal the number of weeks. Thus, \(x = \frac{24}{3} = 8\), indicating he has been doing this for 8 weeks. This matches 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?
- This scenario represents \(x = 24\) for each person, so \(3x = y\) (where \(y\) is the total stickers), but does not express \(3x = 24\) since the total is not the same structure.
Based on the analysis, 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?
1 answer