SOLUTION: 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 as many books as the second o

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Question 1138269: 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 as many books as the second one. How many books are there on each shelf?

Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source):
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let x equal the number of books on the first shelf.
let y equal the number of books on the second shelf.

if half of the books from the second shelf were relocated to the first shelf, then the first shelf would contain 4 times as many books as the second shelf.

the equation for this is:

x + 1/2 * y = 4 * (1/2 * y).

simplify to get x + 1/2 * y = 2 * y.

multiply both sides of this equation by 2 to get 2x + y = 4y.

subtract y from both sides of the equation to get 2x = 3y.

solve for y in the first equation of x + y = 55 to get y = 55 - x.

replace y with 55 - x in the equation of 2x = 3y to get 2x = 3 * (55 - x)

simplify to get 2x = 165 - 3x

add 3x to both sides of this equation to get 5x = 165.

solve for x to get x = 33.

since x + y = 55, then y = 22.

you have x = 33 and y = 22.

x + y = 33 + 22 = 55

take away half of y and add it to x to get x = 44, leaving y to be equal to 11.

44 is equal to 4 * 11, confirming the solution is correct.

there were originally 33 books on the first shelf and 22 books on the second shelf.

after the relocation, there are 44 books on the first shelf and 11 books on the second shelf.

Answer by ikleyn(52798) (Show Source):
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.

Let x = # of books at the SECOND shelf; then the number of book at the FIRST shelf is (55-x). After relocation SECOND shelf has books, while the FIRST shelf has (55-x+ x/2}}} = (55-x/2) books. The condition says = , or, equivalently, 2x = Multiply bu 2 both sides, simplify and solve for x 4x = 110 - x 4x + x = 110 5x = 110 x = 110/5 = 22. Answer. 22 books at the second shelf and the rest, (55-22) = 33 at the first shelf.

Solved.