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April 18th, 2019, 11:41 AM  #1 
Senior Member Joined: Jan 2012 Posts: 741 Thanks: 7  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. 
April 18th, 2019, 12:45 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,427 Thanks: 1314 
$b = 2pn$ $pn = 3pl$ $3(b + pn + pl) = 4000$ $3(6pl + 3pl + pl) = 4000$ $30pl = 4000$ $pl = \dfrac{400}{3}$ $pn = 400$ 
April 18th, 2019, 06:16 PM  #3 
Senior Member Joined: Jan 2012 Posts: 741 Thanks: 7 
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. 
April 18th, 2019, 06:31 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,412 Thanks: 1024  
April 19th, 2019, 02:03 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,623 Thanks: 2076 
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. 
April 19th, 2019, 01:53 PM  #6 
Senior Member Joined: Jan 2012 Posts: 741 Thanks: 7  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?

April 19th, 2019, 06:09 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,412 Thanks: 1024  
April 26th, 2019, 02:28 AM  #8  
Senior Member Joined: Jan 2012 Posts: 741 Thanks: 7  Quote:
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  
April 26th, 2019, 09:58 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 20,623 Thanks: 2076  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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