The equation \(3x = 24\) can be solved by dividing both sides by 3 to find \(x\):
\[ x = \frac{24}{3} = 8 \]
Now let's analyze each option based on this calculation.
A. 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?
- Here, if Andrew lists 3 words per week, then the number of weeks \(x\) would be: \[ 3x = 24 \Rightarrow x = 8 \] This option fits.
B. 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 situation does not fit \(3x = 24\), as it describes a different relationship (1/3 of surveyed students equals 24).
C. 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 relationship can be described as \(3 \times (cost~of~shirt) = cost~of~shoes\). If the cost of the shirt is $24, then this equation does not fit \(3x = 24\) as formulated.
D. Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?
- This describes a scenario where the total number of stickers is \(3 \times x = total~stickers\), if each received 24 stickers, then it does not fit \(3x = 24\).
The correct answer is:
A. 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?