Math CentralQuandaries & Queries


Question from Fay:

Given math homework problem of: Gary and Larry given 2 numbers and told to add together. Gary subtracted and got 14. Larry multiplied and got 799. I tried substitution:
X-Y=14 and X x Y=799
X= Y+14
(Y+14) Y=799 and here I'm stuck at Y squared+14 Y= 799
using substitution I got 47x17=799 but not 14b when subtracted. HELP?????

Hi Fay,

I think there is an error in this problem.

$47 \times 17 = 799$ but the difference is 30. Since 47 and 17 are primes 799 can only be factored as $1 \times 799$ and $47 \times 17$ so if you are looking for integers there is no solution to the problem. If 799 is replaced by 792 there is a solution, as $792 = 22 \times 36.$

The equation

\[Y^2 + 14 Y - 799=0\]

doesn't factor and the general quadratic gives roots that are not integers, in fact they are irrational. This does give you a solution to the problem but I don't think that is what was intended.

I hope this helps,

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