A copy machine makes 32 copies per minute. How many copies does it make in 3 minutes and 45 seconds?

Question

I'm having trouble with these kinds of questions.  I made this question up so I could get a hang of it.  If you could answer this question it would be great!

Answer 1

"These kinds of questions" involve what's called "unit rate" or involve "proportions."  In either case, the units are extremely important.

 

"32 copies per minute" is a unit rate.  That is, "how many of these for one of those?"

 

In this problem, "per" means division.  There are 60 seconds per minute, so this is:

   (32 copies) / (60 seconds)

 

The question asks, "How many copies does it make in 3 minutes and 45 seconds?"

 

Note that (copies/minute)*minute results in copies because the minutes cancel out.  So,

    ( (32 copies) / (60 seconds) ) * ( 225 seconds)  = 120 copies

 

This can also be set up as a proportion (because the same rate is assumed).

     Let x = number of copies

 

     32/60 copies/second  =  x / (225 seconds)

     x = ((32 copies) / (60 seconds))*(225 seconds)               [cross-multiply] 

     x = 120 copies

Answer 2

45 seconds = 45/60 minutes = 3/4 minutes

 

(3 3/4 minutes)(32 copies per minute)

 

Can you multiply 

(3 3/4)(32) = (15/4)(32) = ______ copies