or
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
An administrative assistant is making some copies. She made 13 one-sided copies and 16 two-sided copies for the V.P. of Marketing, which took a total of 93 seconds. Next, she made 13 one-sided copies and 50 two-sided copies for the Director of Sales, which took 263 seconds. How long does it take to make each type of copy?
It takes
seconds to make a one-sided copy and
seconds to make a two-sided copy.
Let x be the time it takes to make a one-sided copy in seconds and y be the time it takes to make a two-sided copy in seconds.
From the given information:
13x + 16y = 93 (equation 1)
13x + 50y = 263 (equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Using the elimination method, we can multiply equation 1 by 50 and equation 2 by 16 to eliminate the x term:
650x + 800y = 4650 (equation 3)
208x + 800y = 4208 (equation 4)
Subtracting equation 4 from equation 3:
(650x - 208x) + (800y - 800y) = (4650 - 4208)
442x = 442
x = 1
Substituting the value of x = 1 into equation 1:
13(1) + 16y = 93
13 + 16y = 93
16y = 93 - 13
16y = 80
y = 5
Therefore, it takes 1 second to make a one-sided copy and 5 seconds to make a two-sided copy.