SOLUTION: The product of two consecutive integers is 9 less than 9 times their sum. Find the integers.
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Question 112422: The product of two consecutive integers is 9 less than 9 times their sum. Find the integers.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If the smaller of the two consecutive integers is x, then the other one must be x + 1.
The product of these two integers is then: x(x+1), and the sum of these two integers is x + (x + 1), or 2x + 1.
Now we can translate the first sentence of the problem into mathematical symbols:
The product of two consecutive integers (x(x + 1)) is (=) 9 times their sum (9(2x + 1)), less 9 (-9). Or,
Now simplify and solve:
, and finally,
or .
This means that the two consecutive integers are either 0 and 1 or 17 and 18.
Check:
, and our first answer checks.
, and the second answer checks also.
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