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September 22nd, 2018, 05:36 AM  #1 
Member Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2  Tom and Nora shared some sweets
Tom and Nora shared some sweets. Nora received 3/5 of the sweets. She gave Tom 8 sweets so that both of them had an equal number of sweets. How many sweets did Tom and Nora share in all? My work: Number of sweets Tom have = T Number of sweets Nora have = N Number of sweets = S [1] We know Tom and Nora shared some sweets. T + N = S [2] Nora received 3/5 of the sweets. She gave Tom 8 sweets so that both of them had an equal number of sweets. 3/5N  8 = 2/5T + 8 Now here is my question, did I do it mathematically correct? From [2], I changed the N and the T to an S so 3/5S  8 = 2/5S + 8 so, S = 80. Is it mathematically correct to change N and T to an S because we are looking for how many sweets their are? 
September 22nd, 2018, 06:26 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond 
No. The final answer and your last equation are correct but N and T are initially being used as the total number of sweets, not how many sweets Tom and Nora had. Solve 3/5S  8 = 1/2S for S. You can obtain that equation from the given information. Last edited by greg1313; September 22nd, 2018 at 06:39 AM. 
September 22nd, 2018, 08:30 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,474 Thanks: 2039 
As Nora started with 60% of the sweets, she gave away 10%, and so there were 80 sweets.

September 22nd, 2018, 09:52 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,319 Thanks: 1023 
Only need 1 variable: t = total sweets 3t/5  8 = 2t/5 + 8 ; multiply by 5: 3t  40 = 2t + 40 t = 80 If they're marshmallows, I want 'em all! 
September 22nd, 2018, 06:23 PM  #5 
Member Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2  

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