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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.An administrative assistant is making some copies. She made one-sided copies and two-sided copies for the V.P. of Marketing, which took a total of seconds. Next, she made one-sided copies and two-sided copies for the Director of Sales, which took 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.
Full solution
Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.An administrative assistant is making some copies. She made one-sided copies and two-sided copies for the V.P. of Marketing, which took a total of seconds. Next, she made one-sided copies and two-sided copies for the Director of Sales, which took 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.
- Define Variables: Define the variables for the time it takes to make each type of copy.Let be the time (in seconds) it takes to make a one-sided copy.Let be the time (in seconds) it takes to make a two-sided copy.
- Write Equations: Write the system of equations based on the given information.For the V.P. of Marketing: one-sided copies and two-sided copies took seconds.For the Director of Sales: one-sided copies and two-sided copies took seconds.
- Eliminate Variable: Decide which variable to eliminate.We can eliminate by subtracting the second equation from the first because the coefficients of are the same in both equations.
- Subtract Equations: Subtract the second equation from the first to eliminate .
- Solve for x: Solve for x.
- Substitute : Substitute the value of into one of the original equations to solve for . Using the second equation:
- Solve for y: Solve for y.
- Check Solution: Check the solution by substituting and into the other original equation.Using the first equation:The solution checks out.
