SOLUTION: a positive integer is 10 more than 6 times another. their product is 464. find the two integers

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Question 983136: a positive integer is 10 more than 6 times another. their product is 464. find the two integers
Answer by ikleyn(52764) About Me  (Show Source):
You can put this solution on YOUR website!

Let  x  be the first unknown integer and  y  be the second unknown integer.
Then you have two equations

system%28x+=+6y+%2B+10%2C%0D%0Axy+=+464%29.

To solve the system,  substitute the first equation into the second one.  You will get

(6y + 10)*y = 464.

Simplify and solve it:

6y%5E2 + 10y = 464,

6y%5E2 + 10y - 464 = 0,

y%5B1%5D = %28-10+%2B+sqrt%2810%5E2+%2B+4%2A6%2A464%29%29%2F12 = %28-10+%2B+106%29%2F12 = 96%2F12 = 8,

y%5B2%5D = %28-10+-+sqrt%2810%5E2+%2B+4%2A6%2A464%29%29%2F12 = %28-10+-+106%29%2F12 = %28-116%29%2F12 = 92%2F3.

Only first root satisfies the condition of the problem  (is integer).

Answer.  The two integers are  8  and  6*8+10 = 58.