Select the correct answer.
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 $x$, the number of minutes it will take Amy to finish typing her paper?
A. $38 x-1,450>76$
B. $38(x+1,450)>4,000$
C. $38 x>4,000$
D. $38 x+1,450>4,000
Answer (2)
Calculate the remaining words needed: 4000 − 1450 = 2550 .
Express the words typed in x minutes: 38 x .
Set up the inequality: 4000"> 1450 + 38 x > 4000 .
The correct inequality is: 4000}"> 38 x + 1450 > 4000 .
Explanation
Problem Analysis Let's analyze the problem. Amy types at an average speed of 38 words per minute and has already typed 1,450 words. Her final paper needs to be more than 4,000 words. We need to find the inequality that represents the number of minutes, x , it will take her to finish the paper.
Calculate Remaining Words First, we need to determine how many more words Amy needs to type. Since the paper must be more than 4,000 words and she has already typed 1,450 words, she needs to type more than 4000 − 1450 = 2550 words.
Words Typed in x Minutes Next, we need to express the number of words Amy types in x minutes. Since she types at a rate of 38 words per minute, in x minutes she will type 38 x words.
Setting up the Inequality Now, we can set up the inequality. The total number of words typed (already typed plus the words typed in x minutes) must be greater than 4,000. So, we have 4000"> 1450 + 38 x > 4000 .
Final Inequality Therefore, the correct inequality is 4000"> 38 x + 1450 > 4000 .
Examples
Imagine you're planning a fundraising event and need to reach a certain financial goal. You've already raised a portion of the money, and you know how much each ticket sale contributes. This problem is similar to figuring out how many more tickets you need to sell to exceed your fundraising target. Understanding inequalities helps in various planning scenarios, such as budgeting, resource allocation, and goal setting, ensuring you meet or exceed your objectives.
The correct inequality representing how long it will take Amy to finish typing her paper is 4000"> 38 x + 1450 > 4000 . This inequality ensures that the total number of words she types exceeds 4,000. Therefore, the answer is option D.
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