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.