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?
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! :)
To solve this problem, we can set up a system of equations based on the given information.
Let's say it takes x seconds to print one page using regular type and y seconds to print one page using bold type.
From the first statement, we know that it takes 1 page using regular type (x seconds) plus 3 pages using bold type (3y seconds) to complete in a total of 23 seconds. Hence, we have the equation:
x + 3y = 23 -- (Equation 1)
From the second statement, we know that it takes 2 pages using regular type (2x seconds) plus 4 pages using bold type (4y seconds) to complete in a total of 34 seconds. Hence, we have the equation:
2x + 4y = 34 -- (Equation 2)
Now, we can solve this system of equations using any suitable method. Let's use the substitution method:
From Equation 1, we can solve for x in terms of y:
x = 23 - 3y
Now, substitute this value of x in Equation 2:
2(23 - 3y) + 4y = 34
Simplify and solve for y:
46 - 6y + 4y = 34
-2y = 34 - 46
-2y = -12
y = 6
Now, substitute this value of y in Equation 1 to find x:
x + 3(6) = 23
x + 18 = 23
x = 23 - 18
x = 5
Therefore, it takes 5 seconds to print one page using regular type and 6 seconds to print one page using bold type.