Problem

1. Write a proportion that represents the problem situation: It takes a copy machine 3 minutes to make 80 copies. At this rate, how long would it take to make 1750 copies? Write your answer in the space provided.

Answer

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Answer

Final Answer: The time it would take for the copy machine to make 1750 copies is \(\boxed{65.625}\) minutes.

Steps

Step 1 :Given that it takes a copy machine 3 minutes to make 80 copies, we are asked to find out how long it would take to make 1750 copies.

Step 2 :We can set up a proportion where the ratio of time to copies is equal for both situations. Let's denote the time it takes to make 80 copies as \(time_{80}\) and the time it takes to make 1750 copies as \(time_{1750}\).

Step 3 :We know that \(time_{80} = 3\) minutes and the number of copies in the first situation is 80 (\(copies_{1} = 80\)) and in the second situation is 1750 (\(copies_{2} = 1750\)).

Step 4 :By setting up the proportion \(\frac{time_{80}}{copies_{1}} = \frac{time_{1750}}{copies_{2}}\), we can solve for \(time_{1750}\).

Step 5 :Substituting the known values into the equation, we get \(\frac{3}{80} = \frac{time_{1750}}{1750}\).

Step 6 :Solving for \(time_{1750}\), we find that \(time_{1750} = 65.625\) minutes.

Step 7 :Final Answer: The time it would take for the copy machine to make 1750 copies is \(\boxed{65.625}\) minutes.

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