
By: parent603 (offline) Monday, February 24 2014 @ 02:20 AM CST (Read 1400 times)



parent603 
Pls help to provide solution to this question.
Thanks alot
Ans 396 books
Mr Jones had a total of 1448 fiction and non fiction books.
He sold 80% of the fiction books and 75% of the non fiction books.
He found he had 52 more fiction books than non fiction books left.
How many non fiction books did he sell?

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Registered: 11/07/11 Posts: 14





By: echeewh (offline) Monday, February 24 2014 @ 02:48 AM CST



echeewh 
Hey <parent603>
Appreciate that you refer to my recently provided solutions to 4 questions found on this post  <Pls help on these questions>  last posted Feb 23. Your question is very similar to those of Q1  3 in that post and you can use either <Work Backward> or <Simultaneous> method to solve it. Hope you can try either method and see how it works for you. Thank you.
Will update the worked solution in due course
//updated Feb25 0630
Following is my worked solution using <Simultaneous> method:
Using <Simultaneous> method, we have ...
<Before>
F + NF = 1448  (1)
<Books Sold>
F: 80% (80/100 = 4/5)
NF: 75% (3/4)
<After>
Given that he had 52 more fiction books (F) than non fiction books (NF) left, we have ...
F  NF = 52
(1/5)F  (1/4)NF = 52  (2)
Common multiple of 5,4 is 20. So ...
(2)x20:
[20 × (1/5)F]  [20 × (1/4)NF] = (20 × 2052)
4F  5NF = 1040  (3)
Comparing (1),(3) and eliminating F, we have ...
(1)x4:
4F + 4NF = 5792  (4)
(4)(3):
4NF + 5NF = 5792  1040
9NF = 4752
NF > 4752 ÷ 9 = 528
NF (sold) = 75% (3/4)
= (3/4) × 528
= 396
=======
Trust this helps.
Do let me know again if there're further clarifications.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 627





By: jo sarah (offline) Monday, February 24 2014 @ 06:19 AM CST



jo sarah 
Mr Jones had a total of 1448 fiction and non fiction books.
He sold 80% of the fiction books and 75% of the non fiction books.
He found he had 52 more fiction books than non fiction books left.
How many non fiction books did he sell?
Solution:
Let the no. of fiction books be 5u [u: units].......since Qn speaks of selling 80%, which is 4/5
and no. of nonfiction books be 4p [p: parts].....since sold 75% which is 3/4
[it is generally easier to convert percentages to fractions, and deal with smaller no.]
............................F...................NF...............[F: fiction books; NF: nonfiction books]
beginning:..........5u...................4p
sold:...................4u...................3p
end (left with):....1u...................1p
And he had 52 more F than NF books in the end,
therefore, 1u = 52 + 1p
[you write this way instead of 1p = 1u  52; because Qn wants NF no. sold; so that you want to find value of 1p]
that means, 5u = 260 + 5p.............[1]
and in beginning, he had 1448 books in total,
which is 5u + 4p = 1448
implies, 260 + 5p + 4p = 1448............[using [1] to replace 5u]
so that, 9p = 1448  260 = 1188
and so, 1p = 132
and he sold 3p = 3 x 132 = 396 nonfiction books.

check:
since 1p = 132, 1u = 184
and 4p + 5u = 528 + 920 = 1448
and you needn't worry about answer key!

Regular Member
Registered: 03/20/12 Posts: 111



