Which of the following can be represented by the equation 3x = 24

Question

?(1 point)
Responses

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?
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?

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

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?
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?

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?

Answer 1

To solve the equation $3x=24$ for $x$, we divide both sides by 3:

$$x=\frac{24}{3}=8$$

Now, let's analyze each of the options to see which can be represented by this equation:

1. Andrew's situation: 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, $x$ represents the number of weeks, and since he picks 3 words each week, $3\times x=24$. This fits the equation.

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

   • Here, each of the three people receives 24 stickers, so $3x=24$ would imply $x$ is the number of stickers each person gets, which is not what the equation represents.

3. Shoes and shirt cost: 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 situation, if the shirt costs 24, we calculate the shoes as $3\times 24$, so it does not fit the equation $3x=24$ for any variable $x$.

4. Survey result: 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?

   • Here, this does not directly fit $3x=24$ and is instead a different kind of equation relating to fractions.

Thus, the correct response 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?