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

Question

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?

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

Andrew picks three words from a dictionary every week and lists theme in his notebook, So far, he has listed 24 words. How many weeks has Andrew been doing this?

Answer 1

To determine which of the situations can be represented by the equation \(3x = 24\), we will analyze each scenario:

1. Survey on favorite subjects:

   • The statement says that one-third of all surveyed students is 24. This can be translated into the equation: \[ \frac{1}{3} \text{(total students)} = 24 \] To represent the number of surveyed students, let \(x\) be the total number of students. This would give us: \[ \frac{1}{3}x = 24 \implies x = 24 \times 3 = 72 \] This does not match the equation \(3x = 24\).

2. Cost of shoes:

   • The shoes cost three times the cost of a shirt. If the cost of the shirt is $24, then the cost of the shoes \(x\) can be represented as: \[ 3x = 24 \] Here \(x\) would be the cost of the shoes, and solving gives: \[ x = \frac{24}{3} = 8 \] This matches the equation \(3x = 24\).

3. Stickers divided among friends:

   • If Rita and her two friends each got 24 stickers, that means there are three people in total: \[ 3 \text{(people)} \times 24 \text{(stickers each)} = 72 \text{ (total stickers)} \] This can be expressed as: \[ 3x = 72 \] So this also does not match \(3x = 24\).

4. Andrew's dictionary words:

   • Andrew picks three words per week. If he has listed 24 words, we can represent this as: \[ 3 \text{(words per week)} \times x \text{(weeks)} = 24 \] Rearranging gives us: \[ 3x = 24 \] So solving this: \[ x = \frac{24}{3} = 8 \] This also matches \(3x = 24\).

Conclusion: The scenarios that can be represented by the equation \(3x = 24\) are:

• The cost of shoes (where \(x\) is the cost of the shoes).
• Andrew listing words from the dictionary (where \(x\) is the number of weeks).

Ultimately, the question asks which of the scenarios can be represented by the equation \(3x = 24\), and the correct contexts are:

• Cost of shoes.
• Andrew's dictionary words.

Answer 2

So which one is it? :3

Answer 3

The equation \(3x = 24\) specifically corresponds to the following two scenarios:

1. The Cost of Shoes: If the cost of a shirt is $24, thus making the cost of the shoes three times that amount. This situation can be directly represented by the equation \(3x = 24\) (where \(x\) is the cost of the shoes).

2. Andrew’s Dictionary Words: If Andrew picks three words each week and has listed a total of 24 words, this is also represented by the equation \(3x = 24\) (where \(x\) is the number of weeks).

So the equation \(3x = 24\) can represent both the cost of the pair of shoes and Andrew's word listing over weeks. If you need to choose only one, then you can select the cost of shoes as a clear economic context or Andrew’s dictionary words based on interest in educational activities.