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Amy types at an average speed of 38 words per minute. She has already typed 1,450 words of her final paper, which will be more than 4,000 words. Which inequality can be used to solve for [tex]$x$[/tex], the number of minutes it will take Amy to finish typing her paper?

A. [tex]$38x - 1,450 \ \textgreater \ 76$[/tex]
B. [tex][tex]$38(x + 1,450) \ \textgreater \ 4,000$[/tex][/tex]
C. [tex]$38x \ \textgreater \ 4,000$[/tex]
D. [tex]$38x + 1,450 \ \textgreater \ 4,000$[/tex]



Answer :

GinnyAnswer
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]