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 34 one-sided copies and 11 two-sided copies for the V.P. of Marketing, which took a total of 135 seconds. Next, she made 23 one-sided copies and 42 two-sided copies for the Director of Sales, which took 195 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.

Question

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 34 one-sided copies and 11 two-sided copies for the V.P. of Marketing, which took a total of 135 seconds. Next, she made 23 one-sided copies and 42 two-sided copies for the Director of Sales, which took 195 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.

Bytelearn · Accepted Answer

Define variables: Define the variables for the time it takes to make each type of copy. Let x be the time (in seconds) it takes to make a one-sided copy. Let y 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: 34 one-sided copies and 11 two-sided copies took 135 seconds. 34x + 11y = 135  For the Director of Sales: 23 one-sided copies and 42 two-sided copies took 195 seconds. 23x + 42y = 195Multiply first equation: Multiply the first equation by a number that will allow us to eliminate one of the variables when we subtract the equations. We can multiply the first equation by 2 to align the coefficients of y with the second equation. (34x + 11y) * 2 = 135 * 2 68x + 22y = 270Subtract equations: Now we have the system of equations: 68x + 22y = 270 23x + 42y = 195 We will subtract the second equation from the first to eliminate y. (68x + 22y) - (23x + 42y) = 270 - 195 68x + 22y - 23x - 42y = 270 - 195Solve for x: Perform the subtraction to solve for x. 68x - 23x + 22y - 42y = 270 - 195 45x - 20y = 75Multiply second equation: We need to find a suitable multiple of the second original equation to eliminate x. We can multiply the second original equation by 2 to align the coefficients of x with the new equation we have. (23x + 42y) * 2 = 195 * 2 46x + 84y = 390Subtract equations: Now we have the system of equations: 45x - 20y = 75 46x + 84y = 390 We will subtract the first equation from the second to eliminate x. (46x + 84y) - (45x - 20y) = 390 - 75 46x - 45x + 84y + 20y = 390 - 75Solve for y: Perform the subtraction to solve for y. 46x - 45x + 84y + 20y = 390 - 75 x + 104y = 315 Since we have only 1x, we made a mistake in our calculations. We need to correct this.

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