The equation \(3x = 24\) can be interpreted in the following way:
To solve for \(x\), you would divide both sides of the equation by 3:
\[ x = \frac{24}{3} = 8 \]
So, \(x = 8\). Let's analyze the options:
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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 fits the equation, as if Andrew lists 3 words each week, the number of weeks (\(x\)) he has been doing this would be \(3x = 24\), implying he has been doing this for 8 weeks.
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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 directly relate to \(3x = 24\) since it calculates the cost of shoes based on the cost of the shirt, not determining how many items were bought.
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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 situation does not fit \(3x = 24\), because it indicates they received 24 stickers each, not determining how many total stickers were equally divided.
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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 implies \( \frac{1}{3} \) of the total students equals 24, and would form the equation \( \frac{1}{3}y = 24 \) rather than \(3x = 24\).
The only option that directly corresponds to 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?