Question 1189395: Please help me solve this problem!!
: A book dealer has books in store of which 1/5 were hardcover books . the dealer sold 2/3 of the books , including 3/4 of the hardcover books . what fraction of the unsold books were hardcover books??
Found 3 solutions by Theo, Octo-pie7, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of books the dealer had.
let h = the number of hard cover books.
1/5 of the books were hard cover.
therefore:
h = 1/5 * x
the dealer sold 2/3 of the books that included 3/4 of the hard cover books.
this means the dealer sold 3/4 * h.
this means the dealer did not sell 1/4 * h.
the fraction of the books that were not sold = 1/3 * x.
the ratio of the number of hard cover books that were not sold to the number of books that were not sold is (1/4 * h) / (1/3 * x).
since h = 1/5 * x, the ratio becomes (1/4 * 1/5 * x) / (1/3 * x).
that becomes (1/20 * x) / (1/3 * x).
that becomes (1/20) / (1/3) which is equal to (1/20) * 3 which is equal to 3/20.
the fraction of the unsold books that were hard cover was 3/20.
to test this out, i created an example.
in the example, i assumed the total number of books was 120.
since the number of hard cover books was 1/5 * the total number of books, then the number of hard cover books was 24.
2/3 of the books were sold, including 3/4 of the hard cover books.
what was sold was:
2/3 * 120 = 80 total books.
this included 3/4 * 24 = 18 hard cover books.
what was not sold was:
1/3 * 120 = 40 total books.
this included 1/4 * 24 = 6 hard cover books.
the ratio of unsold hard cover books to unsold books was 6/40 = 3/20.
this confirms the fraction is correct.
your solution is that the fraction of unsold books that were hard cover books is 3/20.
Answer by Octo-pie7(11)  (Show Source):
You can put this solution on YOUR website! Assumption : Let z = 120 be the
totallity of all the books:
1/5(120) = 24 => no. of hardcover books
4/5(120) = 96 => no. of softcover books
2/3(120) = 80 => sold books, in w/c
3/4(24) = 18 are hardcover books
of remaining hardcover books:
x = 24 - 18 = 6
of remaining books :
y - 120 - 80 = 40
let r be the fractional part of
unsold books:
r = 6/40 = 3/20
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Tutor octo-pie didn't answer the question that was asked....
The other tutor has the right answer, but it takes a long time for the reader to get through his treatment of the problem.
x = original number of books
(1/5)x = original number of hardcover books
(4/5)x = original number of other books
(3/4)*(1/5)x = (3/20)x = number of hardcover books sold
(1/4)*(1/5)x = (1/20)x = number of hardcover books unsold
(2/3)x = number of books sold
(1/3)x = number of books unsold
The fraction of unsold books that are hardcover is (number of unsold hardcover) divided by (total number unsold)
ANSWER: 3/20 of the unsold books were hardcover
|
|
|
