To determine which scenario can be represented by the equation \(3x = 2\), we need to 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 can be represented by the equation \( \text{cost of shoes} = 3(\text{cost of shirt}) \). If the shirt costs $24, then the equation would be \( \text{cost of shoes} = 3(24) = 72 \). This doesn't match \(3x = 2\).
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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?
Let \(x\) be the total number of stickers. Since there are three people (Rita and two friends), they each received 24 stickers: \(x = 3 \times 24\). This solves to \(x = 72\) and can be expressed in a different form, but it doesn’t correspond to \(3x = 2\).
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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?
Let \(x\) represent the total number of students surveyed. The equation based on the given information would be \(\frac{x}{3} = 24\). When we multiply through by 3, we get \(x = 72\). This can also be rearranged to \(x = 72\), which is not represented by \(3x = 2\).
Based on the analysis of the above scenarios, none of them are represented by the equation \(3x = 2\). The equation \(3x = 2\) simplifies to \(x = \frac{2}{3}\), which does not fit any of the provided responses. However, if were to adjust the context of the queries, we could fit different situations where one variable represents a fraction or decimal value, but as it stands none provided match.
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