The equation \(3x = 24\) can be solved for \(x\) by dividing both sides by 3:
\[ x = \frac{24}{3} = 8 \]
This means that \(x\) represents a quantity that, when multiplied by 3, gives 24.
Now, let's analyze each of the options:
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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 would imply \(3 \times 24 = 72\), which does not match the equation \(3x = 24\). -
Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?
Here, if three people received 24 stickers each, the total number of stickers is \(3x = 3 \times 24 = 72\), which does not match the equation \(3x = 24\). -
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?
In this case, if Andrew picks 3 words each week, the equation \(3x = 24\) applies, where \(x\) is the number of weeks. Solving \(3x = 24\) gives \(x = 8\). This is a match. -
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 would translate to \( \frac{1}{3} \text{ of the total} = 24\). If we let \(y\) be the total number of students surveyed, then \(\frac{y}{3} = 24\), which leads to \(y = 72\). This does not match \(3x = 24\).
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?