Question

Two positive integers are 3 units apart on a number line. Their product is 108.

Which equation can be used to solve for m, the greater integer?

m(m – 3) = 108
m(m + 3) = 108
(m + 3)(m – 3) = 108
(m – 12)(m – 9) = 108

Answer 1

To solve the problem, let's denote the two positive integers as \( m \) (the greater integer) and \( n \) (the lesser integer). According to the problem, we know that:

1. The two integers are 3 units apart, which can be expressed as:
\[
m - n = 3
\]
From this, we can express \( n \) in terms of \( m \):
\[
n = m - 3
\]

2. Their product is 108:
\[
m \cdot n = 108
\]

Substituting \( n \) from the first equation into the second equation gives:
\[
m(m - 3) = 108
\]

Therefore, the correct equation to solve for \( m \) (the greater integer) is:
\[
\boxed{m(m - 3) = 108}
\]