Let's break down the question and solve it step-by-step to find the correct answer.
1. Time to Shape Pots:
- The artist takes 3 minutes to shape each pot.
- If there are [tex]\( p \)[/tex] pots, the time to shape all pots is [tex]\( 3 \times p \)[/tex] minutes.
2. Time to Fire Pots:
- It takes 10 minutes to fire one batch of pots, regardless of the number of pots.
3. Total Time:
- The total time is the sum of the time to shape the pots and the time to fire the pots.
- Therefore, the total time [tex]\( T \)[/tex] can be represented by the expression:
[tex]\[
T = 3p + 10
\][/tex]
4. Time for 10 Pots:
- We need to substitute [tex]\( p = 10 \)[/tex] into the expression to find the total time for 10 pots.
- Substituting [tex]\( p = 10 \)[/tex]:
[tex]\[
T = 3(10) + 10
\][/tex]
[tex]\[
T = 30 + 10
\][/tex]
[tex]\[
T = 40
\][/tex]
So, the correct expression is [tex]\( 3p + 10 \)[/tex] and the time it takes to shape and fire a batch of 10 pots is 40 minutes.
Reviewing the given choices:
- A. The expression is [tex]\( 3 \)[/tex]. It takes 30 minutes to shape and fire 10 pots. (Incorrect)
- B. The expression is [tex]\( 3p - 10 \)[/tex]. It takes 20 minutes to shape and fire 10 pots. (Incorrect)
- C. The expression is [tex]\( 3(p + 10) \)[/tex]. It takes 60 minutes to shape and fire 10 pots. (Incorrect)
- D. The expression is [tex]\( 3p + 10 \)[/tex]. It takes 40 minutes to shape and fire 10 pots. (Correct)
Thus, the correct answer is:
D. The expression is [tex]\( 3p + 10 \)[/tex]. It takes 40 minutes to shape and fire 10 pots.
