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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 45 books. There were twice as many large boxes sent as small boxes, which altogether can hold 440 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.

Answer :

In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

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

              y = 2x

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

                20x + 45y = 440

                      y = 2x

Learn more about linear equation

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