Write a system of equations to describe the situation below, solve using elimination, and in the blanks An administrative assistant is making some copiesShe made 41 one-sided coples and 11 twosided copies for the VR of Marketing, which took a total of 74 seconds. Next, she made 31 one- sided copies and 23 two-sided copies for the Director of Sales, which took 100 secondsHow long does it take to make each type of copy? takes seconds to make a one- sided copy and seconds to make a two -sided copy

Question

Write a system of equations to describe the situation below, solve using elimination, and in the blanks An administrative assistant is making some copiesShe made 41 one-sided coples and 11 twosided copies for the VR of Marketing, which took a total of 74 seconds. Next, she made 31 one- sided copies and 23 two-sided copies for the Director of Sales, which took 100 secondsHow long does it take to make each type of copy? takes seconds to make a one- sided copy and seconds to make a two -sided copy

Answer 1

Let x be the time it takes to make a one-sided copy and y be the time it takes to make a two-sided copy.

For the VR of Marketing:
41x + 11y = 74

For the Director of Sales:
31x + 23y = 100

Now, we will solve this system of equations using elimination method.

Multiply the first equation by 31 and the second equation by 41 to eliminate x:

(41)(41x) + (41)(11y) = (41)(74)
(31)(31x) + (31)(23y) = (31)(100)

1681x + 451y = 3034
961x + 713y = 3100

Now, multiply the first equation by 961 and the second equation by 1681 to eliminate y:

(961)(1681x) + (961)(451y) = (961)(3034)
(1681)(961x) + (1681)(713y) = (1681)(3100)

1604841x + 859111y = 2910534
1618441x + 1204693y = 5203100

Now, subtract the first equation from the second equation:

1618441x + 1204693y - 1604841x - 859111y = 5203100 - 2910534
13600x + 345582y = 2292566

Now, we have a new equation:
13600x + 345582y = 2292566

Now, solve for x and y in this new equation:

13600x + 345582y = 2292566
13600x = 2292566 - 345582y
x = (2292566 - 345582y) / 13600

Using the values of x in either of the original equations, we can solve for y. Finally, plug the value of y back into either of the original equations to solve for x.