To solve this problem, we need to set up an equation that accurately represents the situation.
1. Understanding the Problem:
- Amy types at an average speed of 38 words per minute.
- She has already typed 1,450 words.
- The final paper will be more than 4,000 words.
2. Define the Variables:
- Let [tex]\( x \)[/tex] be the number of minutes she needs to type to finish the paper.
3. Formulating the Inequality:
- Since we need to find out how much more time Amy needs to finish typing the paper, we will focus on the remaining words that she needs to type.
- The total number of words she will have typed after [tex]\( x \)[/tex] more minutes is given by the sum of the words already typed and the words typed in [tex]\( x \)[/tex] minutes. This can be written as:
[tex]\[
\text{Total words} = 1450 + 38x
\][/tex]
- According to the problem, this total must be more than 4,000 words:
[tex]\[
1450 + 38x > 4000
\][/tex]
4. Identifying the Correct Inequality:
- The inequality representing this situation is:
[tex]\[
38x + 1450 > 4000
\][/tex]
Therefore, the correct answer is:
D. [tex]\( 38x + 1,450 > 4,000 \)[/tex]
