The Product of Two Consecutive Integers Problem

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From the CSET Study Guide

Teacher candidates preparing for the CSET Multiple Subjects need to be ready to solve word problems for the subtest 2 Math portion of the exam.

Another type of word problem that has a high probability of appearing is the two consecutive integers problem.

Example:

The product of two consecutive negative even integers is 120. Find the numbers.

Let the first number be n. Let the second number be n + 2 (because even integers must be 2 apart (-2, -4, -6, etc.))

(n)(n+2) = 120

n² + 2n = 120

n² + 2n – 120 = 0

Here we have a quadratic equation to solve. What two numbers when added together equal 2 and when multiplied together equal -120?

Answer: 12, -10.

(n + 12)(n – 10) = 0

So the solutions are n = -12 and n = 10. Because the numbers we are looking for are negative, we can ignore n = 10 and take n = -12 and plug into our second number equation (n + 2) to find the second number.

n + 2 = -12 + 2 = -10. So the answer is the numbers are -10 and -12.

By Peter Lorison

http://www.ACEtheCSET.com

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