February 29th, 2016, 08:36 AM  #1 
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  One number is four more than five times another. If their sum is decreased by six....
One number is four more than five times another. If their sum is decreased by six, the result is ten. Find the numbers. I tried to write the equation from reading this. Is this anywhere near close? x+4+5x6=10 Thanks. Last edited by skipjack; February 29th, 2016 at 10:07 PM. 
February 29th, 2016, 08:49 AM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,146 Thanks: 1003  Quote:
Then test it yourself by substituting...  
February 29th, 2016, 09:13 AM  #3  
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  Quote:
and both this time, and last time I can get the first number being 2. yet then I go 2 plus 4 =6 * 5 is 30 6 =24 so not yet figuring out why it is not working for me.  
February 29th, 2016, 09:18 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,623 Thanks: 2611 Math Focus: Mainly analysis and algebra 
First of all, you have two numbers. Call them $x$ and $y$. The information gives you two equations relating $x$, $y$ and numbers you are given. See if you can build those equations from the text of the question. 
February 29th, 2016, 09:31 AM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,146 Thanks: 1003  Quote:
"One number is four more than five times another." other number= 5*2 + 4 = 14 ; OK? "If their sum is decreased by six, the result is ten." sum = 2 + 14 = 16 16  6 = 10 : Bingo! You're correct  
February 29th, 2016, 09:50 AM  #6  
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  Quote:
Other number is 4+5x (x + 4+5x)6 = 10 The only difference is brackets. Continue.  
February 29th, 2016, 10:24 AM  #7 
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  Thanks i think it was the sum part that really confused me. Was not sure what they meant by that. but now I will try to remember they mean for me to add the 2 numbers I end finding after solving the problem not before solving the problem.

February 29th, 2016, 10:30 AM  #8 
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  
February 29th, 2016, 11:02 AM  #9  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,146 Thanks: 1003  Quote:
There's no multiplication there; just remove the brackets: x + 4 + 5x  6 = 10 6x = 10  4 + 6 6x = 12 x = 2  
February 29th, 2016, 11:05 AM  #10 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,623 Thanks: 2611 Math Focus: Mainly analysis and algebra 
If you write that you have two numbers $x$ and $y$, then you get two equations $y = 4+5x$ and $x+y  6= 10$. If you have learned how to solve simultaneous equations, this is not too difficult to solve (indeed one approach gives you exactly the equation that Denis was working you through. The important thing is to be able to build the equations. To understand what the sentences tell you and be confident that you have written it down correctly. The rest is relatively simple algebra. 

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decreased, number, sum, times 
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