Select the correct answer.

The product of two integers is [tex]$112$[/tex]. One number is four more than three times the other. Which of the following equations could be used to find one of the numbers?

A. [tex]3x^2 + 4x = 112[/tex]
B. [tex]3x^2 + 4 = 112[/tex]
C. [tex]4x^2 + 3x = 112[/tex]
D. [tex]4x^2 + 3 = 112[/tex]

Sure, let's solve the problem step by step.

1. Identify the variables:
- Let one of the integers be [tex]$ x $[/tex].
- Let the other integer be [tex]$ y $[/tex].

2. Use the given relationships:
- The product of the two integers is 112, so we have:
[tex]\[
x \cdot y = 112
\][/tex]
- One number [tex]$ y $[/tex] is four more than three times the other number [tex]$ x $[/tex], which gives us:
[tex]\[
y = 3x + 4
\][/tex]

3. Substitute [tex]$ y $[/tex] in the product equation:
- Substitute [tex]$ y = 3x + 4 $[/tex] into [tex]$ x \cdot y = 112 $[/tex]:
[tex]\[
x \cdot (3x + 4) = 112
\][/tex]

4. Expand and simplify the equation:
- Multiply [tex]$ x $[/tex] with each term inside the parentheses:
[tex]\[
3x^2 + 4x = 112
\][/tex]

5. Resulting equation:
- The equation that can be used to find one of the numbers is:
[tex]\[
3x^2 + 4x = 112
\][/tex]

6. Conclusion:
- From the steps above, we can see that the correct equation is:
[tex]\[
3x^2 + 4x = 112
\][/tex]

Therefore, the correct answer is:
[tex]\[
\boxed{A. \ 3x^2 + 4x = 112}
\][/tex]