To evaluate which situation can be represented by the equation \(3x = 24\), we need to determine if the equation reflects the relationships described in the responses.
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For the first scenario: "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 implies \( \frac{1}{3} \text{ of students} = 24 \). Therefore, \( x = \frac{24}{1/3} = 24 \times 3 = 72 \), not \( 3x = 24 \).
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For the second scenario: "Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?"
- Here, \( \text{Total stickers} = 3 \times 24 \), or \( 3x = 72 \), not \( 3x = 24\).
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For the third scenario: "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 means \( 3 \text{ words/week} \times x \text{ weeks} = 24 \). Thus, the equation can be framed as \( 3x = 24\).
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For the fourth scenario: "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, the cost of the shoes would be \( 3 \times 24 = 72 \), not \( 3x = 24 \).
Thus, the correct response that can be represented by the equation \(3x = 24\) 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