The equation \(3x = 24\) can be solved for \(x\) by dividing both sides by 3:
\[ x = \frac{24}{3} = 8 \]
Now, let's analyze each response to determine which one corresponds to this solution:
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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?
- In this scenario, there are 3 people, and if each received 24 stickers, the total would be \(3 \times 24 = 72\), not corresponding to our equation.
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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?
- Here, if Andrew lists 3 words per week and has 24 words total, we can find the number of weeks he has been doing this by solving \(3x = 24\). Thus, \(x = 8\), meaning Andrew has been doing this for 8 weeks. This corresponds to our 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?
- If the shirt costs $24, the shoes would cost \(3 \times 24 = 72\). This does not correspond to the equation either.
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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?
- In this case, if 24 students represent one-third of the total surveyed, we can set up the equation \( \frac{x}{3} = 24\), which simplifies to \(x = 24 \times 3 = 72\). This does not correspond to our equation.
The only option that matches the equation \(3x = 24\) is the second one about Andrew:
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?