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Two shelves contain 55 books. if half of the books from the second shelf were relocated to the first shelf, then the first shelf would contain 4 times more books than the second one. how many books are there on each shelf?

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If we let x and y be the number of books in each of the shelves, respectively. Then, we generate the equation that best shows the scenario as the following system of linear equations. 
                                x + y = 55
                               x + 0.5y = 4(0.5y)
Solving for the values of x and y will give us the answers of,
                                x = 33
                                y = 22
Then, the number of books in each shelves are 33 and 22, respectively.

Answer:

Books in shelf one are 33 and in shelf two are 22.

Step-by-step explanation:

Let the two shelves contain x and y books.

So from first statement of the question

x + y = 55-------------(1)

\(\frac{y}{2}+x=4(\frac{y}{2})\)

y + 2x = 4y

3y = 2x ⇒ \(x=\frac{3}{2}y\)-------(2)

Now we put the value of x from equation 2 to equation 1

\(\frac{3}{2}y+y=55\)

\(\frac{5}{2}y=55\)

y = 22

Since x + y = 55 ⇒ 22 + x = 55

x = 33

So shelf one is having 33 books and shelf two is having 22 books.

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