Solve the problem.
-The product of two consecutive integers is 9 less than 9 times their sum. Find the integers.
A) 0, 1 or 17, 18
B) 0, 1 or 18, 19
C) 0, 1
D) 17, 18

Question

Quizplus · Accepted Answer

Let the two consecutive integers be $x$ and $x+1$. Their product is $x(x+1)$, and their sum is $x + (x+1) = 2x + 1$. The equation based on the given information is $x(x+1) = 9(2x+1) - 9$. Simplifying, we get $x^2 + x = 18x + 9 - 9$, which simplifies to $x^2 - 17x = 0$. Factoring out $x$, we get $x(x - 17) = 0$, giving us $x = 0$ or $x = 17$. Therefore, the pairs of integers are $0, 1$ and $17, 18$.

Solve the Problem. -The Product of Two Consecutive Integers Is 9 Less Than