Question 1040575: Hi,
I've been trying to solve a word problem but can't figure out how to do it. I've turned the problem into a polynomial which I solved with the quadratic rule but it doesn't give the correct results.
Here's the original problem:
"I saw you at the races, said Steve. Who was the boyfriend? Boyfriend? That's my dad! Pam laughed. But you like puzzles, so here's one. If you add his age to the square of mine, you get just three quarters of my age multiplied by the difference between his age and mine."
I assumed Pam was 'x' and her dad was 'y'.
From the wording, I came up with this:
x^2 + y = 0.75 * ( x * ( y - x ) )
multiplying both sides by 4 gives:
4x^2 + 4y = 3 * ( x * ( y - x ) )
=>
4x^2 + 4y = 3 * ( xy - x^2 )
=>
4x^2 + 4y = 3xy - 3x^2
=>
7x^2 + 4y = 3xy
=>
7x^2 + 4y - 3xy = 0
At this point I tried to divide by y to give a normal quadratic I could solve:
7z - 3x + 4 = 0 (assuming z was equal to x/y)
My problem is that solving this doesn't give the correct results which I know to be x=20,y=50. If I graph the equation the roots aren't right either and the equation seems to be solvable with multiple values. I'm a bit of a maths novice so I'm not sure where I've gone wrong!
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
Do you see, from the very beginning you have only one equation for two unknowns.
It is not enough to get the unique solution.
This situation will not change even if you transform your equation many times.
So, your transformations of the equation are correct, but you can not get a unique solution, because the input info is not enough.
That's all.
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