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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 30 books. There were 4 times as many large boxes sent as small boxes, which altogether can hold 280 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.

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luisejr77

Answer:

[tex]\left \{ {{20x+30y=280} \atop {y=4x}} \right.[/tex]

Where [tex]x[/tex] is the number of small boxes sent and [tex]y[/tex] is the number of large boxes sent.

Step-by-step explanation:

Let be [tex]x[/tex] the number of small boxes sent and [tex]y[/tex] the number of large boxes sent.

Since each small box can hold 20 books ([tex]20x[/tex]), each large box can hold 30 books ([tex]30y[/tex])and altogether can hold a total of 280 books, we can write the following equation to represent this:

[tex]20x+30y=280[/tex]

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation:

[tex]y=4x[/tex]

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is:

[tex]\left \{ {{20x+30y=280} \atop {y=4x}} \right.[/tex]

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