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?
A. $m(m-3)=108$
B. $m(m+3)=108$
C. $(m+3)(m-3)=108$
D. $(m-12)(m-9)=108$

Let m be the greater integer and n be the smaller integer.
Express the smaller integer in terms of the greater integer: n = m − 3 .
Set up the equation for the product of the two integers: m ( m − 3 ) = 108 .
The equation to solve for m is m ( m − 3 ) = 108 ​ .

Explanation

Finding the Equation Let m be the greater integer and n be the smaller integer. Since the two integers are 3 units apart, we have m − n = 3 , so n = m − 3 . The product of the two integers is 108, so mn = 108 . Substituting n = m − 3 into the equation mn = 108 gives m ( m − 3 ) = 108 . Therefore, the equation to solve for m is m ( m − 3 ) = 108 .

Examples
Understanding how to set up equations from word problems is a fundamental skill in algebra. For example, imagine you are designing a rectangular garden where the length is 3 feet longer than the width, and the total area of the garden is 108 square feet. By setting up an equation similar to the one in this problem, you can determine the dimensions of the garden. This type of problem-solving is applicable in various real-world scenarios, such as designing layouts, managing resources, and optimizing processes.

Answered by GinnyAnswer | 2025-07-03

The equation that can be used to solve for m , the greater integer, is m ( m − 3 ) = 108 . This is derived from the condition that the two integers are 3 units apart. Thus, the answer is A ​ .
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Answered by Anonymous | 2025-07-04