The equation \(3x = 24\) can be understood in terms of solving for \(x\). In this equation, \(3x\) indicates that \(x\) is being multiplied by 3.
We can analyze each response:
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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 translates to \( \frac{1}{3} \text{(total surveyed)} = 24 \), which would be represented as \(x/3 = 24\) (or \(x = 72\)). Thus, this does not match 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?
- This translates to \( x/3 = 24 \) (where \(x\) is the total number of stickers Rita bought). This would also solve to \(x = 72\), so it does not match the equation.
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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 can be written as \(3x = 24\) (where \(x\) is the cost of the shirt). However, it should actually be \(3(24) = x\) or \(x = 72\). This matches with the multiplicative scenario, but in reverse. It does not match our equation directly either.
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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 scenarios translates to \(3x = 24\) (3 words per week). Solving gives \(x = 8\), which fits our equation perfectly.
Thus, the correct representation of 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