Question 1003379: one book shelf contains 5 times as many book as another book shelf. when 20 books were moved from the first to the second, the first had 3 times as much as the second. how many books did each have originally?
Answer by maxitee(11)   (Show Source):
You can put this solution on YOUR website! Let's take the First Shelf as Y
Let's take the second Shelf as X
From the question, Originally; Y = 5X
However, upon removing 20 from Y and adding it to X we now have a new Shelf arrangement and we shall call it Z.
Z can be expressed as;
Z = X + 20
From the latter part of the question we can clearly write a new equation after the subtraction/addition from/to Y and X respectively. Whereas Y is thrice the new Shelf arrangment(Z).
Y-20 = 3Z (Where Z is X+20)
Y-20 = 3(X+20)
Y-20=3X + 60
Remember that, Y = 5X, Therefore we substitute Y for X in the above equation.
5X - 20 = 3X + 60.
Solving the above linear equation gives X as.
X= 40.
If X is 40 therefore Y = 5*40
Y= 200.
The first shelf originally had 200 Books while the second originally had 40 Books.
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