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February 28th, 2014, 07:52 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, 08:06 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,807 Thanks: 1045 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, 08:08 AM  #3 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,312 Thanks: 115  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, 08:25 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 = b5" and "7x = b+3" how did you end up with 8 boys and 53 sweets?

February 28th, 2014, 08:32 AM  #5 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,312 Thanks: 115  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, 10:48 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, 10:55 AM  #7 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,312 Thanks: 115  Re: Boys and some Sweets puzzle
That is step by step, I'm sorry to say!

February 28th, 2014, 11:00 AM  #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, 05:30 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, 05:53 AM  #10 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,807 Thanks: 1045 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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