Which of the following can be represented by the equation 3x = 24?(1 point)

Question

Responses

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?

Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?

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?

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?

Answer 1

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, results in 24.

Now, let's examine the options provided:

1. 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?

   • In this case, if we assign the cost of the shirt to \(x\), then the cost of the shoes would be \(3x\). If the shirt costs $24, then this is not represented by the equation \(3x = 24\) because we're looking for how much the shoes cost based on the shirt’s cost, not the other way around.

2. Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?

   • Here, the total number of stickers can be calculated as \(3\) (the three friends) times \(x\), where \(x\) is the number of stickers each one received (24). Thus, \(3x = 72\), which does not fit the equation given.

3. 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 can be represented mathematically as \(\frac{1}{3} \text{ (total surveyed)} = 24\). If we let \(x\) equal the total number of surveyed students, then we have \(\frac{x}{3} = 24\), or \(x = 24 \cdot 3 = 72\), which aligns with the equation \(3x = 72\), not \(3x = 24\).

4. 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, the total number of words can be described by \(3 \cdot \text{(number of weeks)} = 24\). If we let \(x\) be the number of weeks, then \(3x = 24\) fits perfectly.

Thus, the correct option that can be represented by 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?