Question

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?

Answer 1

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

Explanation:

Let the two shelves contain x and y books.

So from first statement of the question

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

`(y)/(2)+x=4((y)/(2))`

y + 2x = 4y

3y = 2x ⇒
`x=(3)/(2)y`-------(2)

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

`(3)/(2)y+y=55`

`(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.

Answer 2

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.