At Elisa's printing company, there are two kinds of printing presses: Model A, which can print 70 books/ day, and model B, which can print 55 books per day. The company owns 14 total printing presses that allow them to print 905 books per day. How many model A presses do they have?

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Mathematics

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At Elisa's printing company, there are two kinds of printing presses: Model A, which can print 70 books/ day, and model B, which can print 55 books per day. The company owns 14 total printing presses that allow them to print 905 books per day. How many model A presses do they have?

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xKelvin xKelvin · Answer 1 · 2025-03-29T02:50:43-04:00

Answer:

9 Model As.

Step-by-step explanation:

Let A represent Press A and let B represent Press B.

So, they own 14 total presses. This means that:

[tex]A+B=14[/tex]

They can print 905 books per day, in other words, since A prints 70 per day and B prints 55 per day:

[tex]70A+55B=905[/tex]

This is now a system of equations. Solve by substitution. From the first equation, subtract B from both sides:

[tex]A=14-B[/tex]

Substitute this into the second equation: "

[tex]70(14-B)+55B=905[/tex]

First, we can divide everything by 5 to simplify things:

[tex]14(14-B)+11B=181[/tex]

Distribute the left:

[tex]196-14B+11B=181[/tex]

Combine like terms:

[tex]-3B+196=181[/tex]

Subtract 196 from both sides:

[tex]-3B=-15[/tex]

Divide both sides by -3

[tex]B=5[/tex]

So, the company has 5 Model B presses.

Which means that the company has 14-5 or 9 Model A presses.

And we're done!