An administrative assistant is making some copies. She made 41 one- sided copies and 11 two-sided copies for the V.P. 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 seconds. How long does it take to make each type of copy ? seconds to make a one-sided copy and seconds to make a It takes two -sided copy
Let x be the time in seconds to make a one-sided copy and y be the time in seconds to make a two-sided copy.
From the information given:
41x + 11(2y) = 74
31x + 23(2y) = 100
Simplify the equations:
41x + 22y = 74
31x + 46y = 100
Now, solve the system of equations to find the values of x and y. One way to do this is by multiplying the first equation by 31 and the second equation by 41, allowing the x coefficients to cancel out:
31(41x + 22y) = 31(74)
41(31x + 46y) = 41(100)
Simplify:
1271x + 682y = 2294
1271x + 1886y = 4100
Subtract the first equation from the second equation:
1204y = 1806
y = 1806 / 1204
y = 1.5
Substitute the value of y back into one of the original equations to solve for x:
41x + 22(1.5) = 74
41x + 33 = 74
41x = 41
x = 41 / 41
x = 1
Therefore, it takes 1 second to make a one-sided copy and 1.5 seconds to make a two-sided copy.