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March 29th, 2017, 01:02 PM  #1 
Newbie Joined: Mar 2017 From: UK Posts: 3 Thanks: 1  Algebra conundrum
Alice is 5 years older than Bob. Let Bob be x. The product of their ages is 149 times the sum of their ages. Write an algebraic expression or equation and work out their ages. Any thoughts??? 
March 29th, 2017, 02:00 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,944 Thanks: 1011 
Let Bob be $b$ $a = b+5$ $a b = 149(a+b)$ you can substitute the first equation into the second and solve for $b$ I leave that to you. 
March 29th, 2017, 02:29 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,967 Thanks: 1607  
March 29th, 2017, 02:37 PM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,751 Thanks: 1401 
$x(x+5) = 149(2x+5)$ solution for $x$ is unreasonable, imho ... Is Bob's age in years? 
March 29th, 2017, 03:13 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 1,944 Thanks: 1011  
March 29th, 2017, 11:58 PM  #6 
Newbie Joined: Mar 2017 From: UK Posts: 3 Thanks: 1 
It was a question in amongst some others on a piece of homework (not mine fortunately  belongs to a 13 year old!) and I was asked to help. I have still not been able to fathom out how to work out how old either Alice or Bob might be!! I went down the same route as you Skeeter but ended up with some ridiculous quadratic that made no sense in relation to ages ... 
March 30th, 2017, 06:18 PM  #7  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,448 Thanks: 832  Quote:
is if product of ages = 6 times the sum. Alice = 15, Bob = 10 or Alice = 2, Bob = 3 : Dad will release him 2 years 3 months from now!  

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