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April 18th, 2019, 11:41 AM   #1
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Find the cost of a set of pens

The cost of a set of books is twice the cost of a set of pens. The cost of a set of pens is three times the cost of a set of pencils. Find the cost of a set of pens if N 4 000 is used in buying the three sets of the items.

cost of a set of books = 2(cost of set pens)
cost of a set pens = 3(cost of set of pencils)
Since the three set of items cost N 4 000, the only equation from the problem is
2( cost of set of pens) + 3( cost of set of pencils) = N 4 000.


I don't know where to go from here.

Last edited by skipjack; April 19th, 2019 at 01:29 AM.
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April 18th, 2019, 12:45 PM   #2
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$b = 2pn$

$pn = 3pl$

$3(b + pn + pl) = 4000$

$3(6pl + 3pl + pl) = 4000$

$30pl = 4000$

$pl = \dfrac{400}{3}$

$pn = 400$
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April 18th, 2019, 06:16 PM   #3
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Please what do the following equations mean? Am going to number them.

$b = 2pn$ ______________________________________ 1

$pn = 3pl$ _____________________________________ 2

$3(b + pn + pl) = 4000$ ________________________ 3

$3(6pl + 3pl + pl) = 4000$ _____________________ 4

$30pl = 4000$

$pl = \dfrac{400}{3}$

$pn = 400$

Again what are the following pn, pl and b?

Last edited by Chikis; April 18th, 2019 at 06:21 PM.
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April 18th, 2019, 06:31 PM   #4
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Quote:
Originally Posted by Chikis View Post
Again what are the following pn, pl and b?
b = sets of books

pn = sets of pen

pl = sets of pencils

Romsek was throwing "the book" at you!!
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April 19th, 2019, 02:03 AM   #5
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If a set of pencils costs M1, a set of pens must cost M3 and a set of books must cost M6,
so the three sets have a total cost of M10.

Hence M10 = ₦4000, and so M3 = ₦1200.

Check:

set of books: ₦2400
set of pens: ₦1200
set of pencils: ₦400

Total: ₦4000, as required.
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April 19th, 2019, 01:53 PM   #6
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Quote:
Originally Posted by romsek View Post
$b = 2pn$

$pn = 3pl$

$3(b + pn + pl) = 4000$

$3(6pl + 3pl + pl) = 4000$

$30pl = 4000$

$pl = \dfrac{400}{3}$

$pn = 400$
Thank you for the equation. I now understand the terms as explained, but is there any way this can be solved using ordinary ratio instead of equations?
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April 19th, 2019, 06:09 PM   #7
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Quote:
Originally Posted by Chikis View Post
...is there any way this can be solved using ordinary ratio instead of equations?
a = a set of books, b = a set of pens, c = a set of pencils.

a = 2b
b = 3c
a + b + c = 4000

RATIOnalize to your heart's content!
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April 26th, 2019, 02:28 AM   #8
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Quote:
Originally Posted by skipjack View Post
If a set of pencils costs M1, a set of pens must cost M3 and a set of books must cost M6,
so the three sets have a total cost of M10.
The assertion above is very correct. It is just like saying that the ratios of set books to set of pens to set of pencils is
6 : 3 : 1 which is true. And that is where my problem lies:
How did you get the ratios of set books, set of pens and set of pencils without using any equation? What did you thinking that brought that ratios to you mind without writing any equation.
If not because I saw and solved the equation:
Quote:
a = a set of books, b = a set of pens, c = a set of pencils.

a = 2b
b = 3c
a + b + c = 4000
I wouldn't have accepted that the given ratio is correct. My greatest problem now is how or what did you think that helped you to compute the ratio even without any equation. Thank you.
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April 26th, 2019, 09:58 AM   #9
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Quote:
Originally Posted by Chikis View Post
The cost of a set of books is twice the cost of a set of pens. The cost of a set of pens is three times the cost of a set of pencils.
The above sentences directly specify the cost ratios 2:1 and 3:1 (for books to pens and pens to pencils respectively), and these imply (by multiplication) the cost ratio 6:1 for books to pencils. This might seem clearer if the books to pens cost ratio is written as 6:3 instead of 2:1, so that one is thinking that 6:3 and 3:1 combine to give 6:1 (or 6:3:1 for all three costs).
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