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 2013 P6 Math SCGS SA2 Q12
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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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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

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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 non-fiction 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: non-fiction 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 non-fiction books. Laughing Out Loud

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

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