A commercial print shop operates two types of high-speed printers, Printer M and Printer N… — GRE General Test

A commercial print shop operates two types of high-speed printers, Printer M and Printer N. Operating simultaneously for $5$ hours, $2$ units of Printer M and $3$ units of Printer N print a total of $5,500$ pages. Operating simultaneously for $4$ hours, $5$ units of Printer M and $2$ units of Printer N print a total of $6,600$ pages. What is the hourly page output of a single Printer M?

Answer: 250 pages per hour

Answer

The hourly page output of a single Printer M is 250 pages per hour.

Dividing each total page output by the corresponding number of hours produces the simplified linear system:

2m + 3n = 1100

and

5m + 2n = 1650

, where

m

and

n

are the hourly rates of Printer M and Printer N. Multiplying the first equation by

2

gives

4m + 6n = 2200

, and multiplying the second equation by

3

gives

15m + 6n = 4950

. Subtracting the two equations eliminates

n

, giving

11m = 2750

, which simplifies to

m = 250

pages per hour.

Step-by-Step Solution

Define variables and write initial algebraic equations based on time and rate.

Let

m

represent the hourly page output of Printer M and

n

represent the hourly page output of Printer N. The total outputs give

5(2m + 3n) = 5500

and

4(5m + 2n) = 6600

Total page output equals total operating time multiplied by the combined hourly output rate.

Simplify the system by dividing each equation by its respective number of hours.

First equation:

2m + 3n = 1100

. Second equation:

5m + 2n = 1650

Simplifying yields a standard system of linear equations representing the combined hourly rate.

Eliminate variable

n

to solve for

m

Multiply

2m + 3n = 1100

2

to get

4m + 6n = 2200

. Multiply

5m + 2n = 1650

3

to get

15m + 6n = 4950

. Subtracting the first modified equation from the second yields

11m = 2750

, so

m = 250

Equating the coefficients of

n

allows direct elimination of

n

when subtracting the equations.

Key Concept

Solving a 2x2 system of linear equations using the method of elimination

Estimated Time:1m 30s

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