Alright, let's carefully analyze the problem step-by-step.
1. Let one integer be [tex]\( x \)[/tex].
2. According to the problem, the other number is four more than three times the first number. So the other integer can be represented as [tex]\( 3x + 4 \)[/tex].
3. The product of these two numbers is given to be 112. Therefore, we can write the equation as:
[tex]\[
x \cdot (3x + 4) = 112
\][/tex]
4. Let's simplify this equation:
[tex]\[
x \cdot (3x + 4) = 112 \implies 3x^2 + 4x = 112
\][/tex]
5. Hence, after simplifying the problem, the equation that represents the relationship between the numbers is:
[tex]\[
3x^2 + 4x = 112
\][/tex]
Therefore, the correct answer is:
A. [tex]\( 3x^2 + 4x = 112 \)[/tex]
