My Math Forum Tom and Nora shared some sweets

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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: 7,958 Thanks: 1146 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. Thanks from xoritos Last edited by greg1313; September 22nd, 2018 at 06:39 AM.
 September 22nd, 2018, 08:30 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,933 Thanks: 2207 As Nora started with 60% of the sweets, she gave away 10%, and so there were 80 sweets. Thanks from greg1313 and xoritos
 September 22nd, 2018, 09:52 AM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 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! Thanks from xoritos
September 22nd, 2018, 06:23 PM   #5
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Quote:
 Originally Posted by greg1313 N and T are initially being used as the total number of sweets, not how many sweets Tom and Nora had. information.
Thank you for this

And thank you to everyone for answering my question

 Tags nora, shared, sweets, tom

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