Question

An impact printer prints 1 page using regular type and 3 pages using bold type in 23 seconds. If the printer prints 2 pages using regular type and 4 pages using bold type in 34 seconds, how long does it take to print 1 page for each typeface?

Answer 1

First, you need to put this info in the form of equations. Let x = regular type and y = bold type. So,

1x + 3y = 23
2x + 4y = 34

Then, multiply one of the equations by a number to cancel out one of the variables. I multiplied the first equation (1x + 3y = 23) by -2, which gives me -2x - 6y = -46. So, now you have:

-2x - 6y = -46
2x + 4y = 34

The -2x and 2x cancel each other out, so now you have:

-6y = -46
4y = 34

which simplifies to:

-2y = -12

which simplifies to:

y = 6

So, it takes 6 seconds to print one bold type page.

Now, you can put the y = 6 back into one of the original equations. I put it into 2x + 4y = 34. So,

2x + 4y = 34
2x + 4(6) = 34
2x + 24 = 34
2x = 10
x = 5

So, it takes 5 seconds to print one regular-type page.

Hope this helps! :)