My Math Forum Boys and some Sweets puzzle

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 February 28th, 2014, 08:52 AM #1 Newbie   Joined: Feb 2014 Posts: 12 Thanks: 0 Boys and some Sweets puzzle Some boys share a bag of sweets. If each boy has 6 sweets, there will be 5 sweets left in the bag. If there were 3 more sweets in the bag, each boy could have exactly 7 sweets. How many sweets were in the bag? ------------------------------------------------------------------------------------------------------------- Could this be a simultaneous equation? Also possible if you showed how you got your answer as this boggled me a bit. Have fun
 February 28th, 2014, 09:06 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,898 Thanks: 1093 Math Focus: Elementary mathematics and beyond Re: Boys and some Sweets puzzle Let x be the number of boys. Let B be the number of sweets in the bag. 6x = B - 5 7x = B + 3 x = 8, B = 53.
 February 28th, 2014, 09:08 AM #3 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Boys and some Sweets puzzle The best way to start off is to let b = number of boys and s = number of sweets. Then, we have: s = 6b + 5 (if every boy has 6 sweets there are 5 left) s + 3 = 7b (if there were 3 more, every boy could have 7) So, yes, that generates two simultaneous equations. Can you solve those? ... I see greg's done it for you!
 February 28th, 2014, 09:25 AM #4 Newbie   Joined: Feb 2014 Posts: 12 Thanks: 0 Re: Boys and some Sweets puzzle Still don't see exactly how you got there though. From forming the equations "6x = b-5" and "7x = b+3" how did you end up with 8 boys and 53 sweets?
 February 28th, 2014, 09:32 AM #5 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Boys and some Sweets puzzle The trick is to subtract one equation from the other: (s + 3) - s = 7b - (6b + 5) 3 = b - 5 b = 8 Then put b into one of the equations: s = 6b + 5 = 48 + 5 = 53
 February 28th, 2014, 11:48 AM #6 Newbie   Joined: Feb 2014 Posts: 12 Thanks: 0 Re: Boys and some Sweets puzzle I still don't quite get it. could you do like step by step?
 February 28th, 2014, 11:55 AM #7 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Boys and some Sweets puzzle That is step by step, I'm sorry to say!
 February 28th, 2014, 12:00 PM #8 Newbie   Joined: Feb 2014 Posts: 12 Thanks: 0 Re: Boys and some Sweets puzzle It may be but it's confusing.
 March 1st, 2014, 06:30 AM #9 Newbie   Joined: Feb 2014 Posts: 12 Thanks: 0 Re: Boys and some Sweets puzzle Another way of doing it would be to; 5 + 3 = 8 boys 6 x 8 = 48 + 5 = 53 sweets.
 March 1st, 2014, 06:53 AM #10 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,898 Thanks: 1093 Math Focus: Elementary mathematics and beyond Re: Boys and some Sweets puzzle 6x = B - 5 7x = B + 3 7x - 6x = (B + 3) - (B - 5) x = 8.

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