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March 29th, 2017, 01:02 PM   #1
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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???
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March 29th, 2017, 02:00 PM   #2
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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.
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March 29th, 2017, 02:29 PM   #3
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Quote:
Originally Posted by danidavinci View Post
Any thoughts???
Did you invent this question?
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March 29th, 2017, 02:37 PM   #4
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$x(x+5) = 149(2x+5)$

solution for $x$ is unreasonable, imho ...

Is Bob's age in years?
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March 29th, 2017, 03:13 PM   #5
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Quote:
Originally Posted by skeeter View Post
$x(x+5) = 149(2x+5)$

solution for $x$ is unreasonable, imho ...
mebbe Bob and Alice have been travelling very close to the speed of light for a while....
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March 29th, 2017, 11:58 PM   #6
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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 ...

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March 30th, 2017, 06:18 PM   #7
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Quote:
Originally Posted by danidavinci View Post
Alice is 5 years older than Bob. Let Bob be x.
The product of their ages is 149 times the sum of their ages.
Only integer solution (keeping both under 100 years old!)
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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