To determine which of the scenarios corresponds to the equation \(3x = 24\), we can rewrite the equation in terms of \(x\):
\[ x = \frac{24}{3} \] \[ x = 8 \]
This means that \(x\) represents the value that, when multiplied by 3, equals 24.
Now let's evaluate 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?
- Here, if the shirt costs $24, then the cost of the shoes would be \(3 \times 24 = 72\). This does not correspond to the equation \(3x = 24\) because \(x\) is not the shirt cost; it's the cost of the shoes.
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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?
- If 24 students represent one-third of the total surveyed, we would let \(x\) be the total students surveyed: \[ \frac{x}{3} = 24 \] This gives us \(x = 24 \times 3 = 72\). This does not correspond to \(3x = 24\) 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?
- If he picks 3 words each week, we can let \(x\) be the number of weeks: \[ 3x = 24 \] This matches the equation \(3x = 24\).
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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?
- If each of them received 24 stickers, and there are three people total, we can express total stickers as \(3x = \text{total stickers}\). Here \(x\) would represent the stickers each person receives, but we are not solving for how many total stickers there are directly via \(3x = 24\).
The scenario that applies directly 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?
1 answer