Pre calculus 20 question

Question

A laser printer prints 24 more sheets per minute than an ink jet printer. If it takes the two printers a total of 14 minutes to print 490 pages, what is the printing rate of the ink jet printer?

 

Answer 1

We have a relationship between the speed of a laser printer and the speed of an inkjet, but we don't actually know how many sheets per minute either prints.  So that gives us two unknowns (x and y)

 

Let x = the number of pages per minute a laser printer produces

Let y = the number of pages per minute an inkjet produces

 

To solve for two unknowns, we need two equations.  The first is that a laser printer prints 24 more sheets per minute than an inkjet:

 

x = y + 24

 

The second equation is that both printers combined take 14 minutes to print 490 pages

 

14*x + 14*y = 490

 

So, substitute the first equation for x into the second equation

 

14*(y + 24) + 14*y = 490

 

14*y + 14*24 + 14*y = 490

 

Combine the two y terms (14*y + 14*y = 28*y) and multiply 14*24

 

28*y + 336 = 490

 

Subtract 336 from both sides

 

28*y + 336 - 336 = 490 - 336

 

28*y = 154

 

Now divide both sides by 28

 

28*y/28 = 154/28

 

y = 5.5

 

Therefore the inkjet printer produces 5.5 sheets per minute

 

You can plug that back into the original two equations to double check your work:

 

x = 24 + 5.5

x = 29.5

 

14*5.5 + 14*29.5 = 490

77 + 413 = 490

490 = 490