Question 1200372: If my mum is twice as old as me. In six years, I will be three years older than half of my mum's age. How old am I?
Found 3 solutions by Theo, ikleyn, Alan3354:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = your mum's age.
y = your age.
your equations that need to be solved simultaneously are:
x = 2y
y + 6 = 1/2 * (x + 6) + 3
simplify the second equation and leave the first equation as is to get:
x = 2y
y + 6 = 1/2 * x + 6
since x = 2y, replace x with that in the second equation to get:
y + 6 = 1/2 * 2 * y + 6
simplify to get:
y + 6 = y + 6
subtract y + 6 from both sides of the equation to get 0 = 0
this means that you have an infinite number of solutions.
confirm by replacing y with any value taken at random.
when y = 25, x = 50 in the first equqtion.
in the second equation, replace y with 25 to get:
y + 6 = 1/2 * (x + 6) becomes 25 + 6 = 1/2 * (50 + 6) + 3 which becomes:
31 = 1/2 * 56 + 3 which becomes:
31 = 28 + 3 which becomes:
31 = 31
you could pick any value for y and yuu will find that you will get a value for x that is true in both equation.
graphically, what you have is that both equations generate the same line on the graph as shown below:
the two equations generated the same line.
any value of y on that line yields a value of x that was equal to 2y.
in general, if all variables in the equations disappear and the equation is true, then you have an infinite number of solutions and, if all variables in the equations disappear and the eqution is not true, then you don't have any solution.
here's a reference.
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:systems-of-equations/x2f8bb11595b61c86:number-of-solutions-to-systems-of-equations/a/number-of-solutions-to-system-of-equations-review
Answer by ikleyn(52803)  (Show Source):
You can put this solution on YOUR website! .
 my mum is twice as old as me.
In six years, I will be three years older than half of my mum's age. How old am I?
~~~~~~~~~~~~~~
If x is my age, then the mum age is 2x years.
In 6 years
x + 6 = 3 +  .
This equation is, actually, an IDENTITY: it is valid for any value of x.
Therefore, it is IMPOSSIBLE to get a unique specific answer: any value of x is good.
DIAGNOSIS. This problem is UNSOLVABLE: it can not be solved and can not be answered
in a reasonable way: any number is the solution.
It has (INFINITELY) many solutions, which for such kind of problems is absurdist
(or, if you wish, is like a death sentence).
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Actually, this " problem " is a TRAP, and the only mathematical content in it is to discover that it is a trap.
Answer by Alan3354(69443)  (Show Source):
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