To solve this problem, let's carefully follow the information given and translate it into an equation:
1. Identify the original price: Let [tex]\( p \)[/tex] be the original price of the car.
2. Understand the price reduction: The car's price was reduced by \[tex]$3000.
3. Identify the new price: After the reduction, the new price of the car is \$[/tex]16,000.
Given these pieces of information, we need to represent the relationship between the original price [tex]\( p \)[/tex], the reduction amount, and the new price.
Let's break it down step-by-step:
1. Start with the original price ([tex]\( p \)[/tex]): This is the starting point.
2. Subtract the reduction amount: The price is reduced by \[tex]$3000. This is indicated by subtracting 3000 from \( p \).
3. Set it equal to the new price: After the reduction, the price becomes \$[/tex]16,000.
Putting these steps together, we have:
[tex]\[ p - 3000 = 16000 \][/tex]
This equation accurately represents the relationship between the original price [tex]\( p \)[/tex], the reduction, and the new price.
Now, let's compare this with the given options:
A. [tex]\( p + 16000 = 3000 \)[/tex]: This option does not correctly represent the situation as it incorrectly adds the new price.
B. [tex]\( 3000 + p = 16000 \)[/tex]: This option also does not correctly represent the situation because it incorrectly adds the reduction amount to the original price.
C. [tex]\( p - 3000 = 16000 \)[/tex]: This option accurately represents the situation as it correctly shows the original price reduced by \[tex]$3000 is equal to the new price of \$[/tex]16,000.
D. [tex]\( 3000 - p = 16000 \)[/tex]: This option does not correctly represent the situation as it incorrectly subtracts the original price from the reduction amount.
Therefore, the correct equation that best represents the described situation is:
[tex]\[ \boxed{C. \, p - 3000 = 16000} \][/tex]
