Question

Is it possible to place 158 books on three shelves so that the first shelf has 8 less books than the second and 5 more books than the third shelf?

Answer 1

Let
x-----------------> books in the first shelf
y-----------------> books in the second shelf
z-----------------> books in the third shelf
we know that
x+y+z=158-------------> equation (1)
x=y-8---------> y=x+8 ------->  equation (2)
x=z+5--------> z=x-5  --------> equation (3)

 substitute (2) and (3) in (1)
x+(x+8)+(x-5)=158--------> 3x=155----------> x=51.7


the number of books in the first shelf (x=51.7) is not a whole number
therefore

the answer is
Is not possible to place the amount of 158 books in the amounts indicated in the problem