Select the correct answer.

The product of two integers is 112. 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. Understanding the Problem Statement:
We are given that the product of two integers is 112, and one number is four more than three times the other number. We need to express this information using an equation and determine which of the given equations fits the situation.

2. Identify Variables:
Let [tex]$ x $[/tex] represent one of the integers. The other integer is described as being four more than three times the first integer. Therefore, we can express the second integer as [tex]$ 3x + 4 $[/tex].

3. Formulate the Equation:
The problem states that the product of these two integers is 112. So, we can write the equation:
[tex]\[
x \times (3x + 4) = 112
\][/tex]

4. Simplify the Equation:
Let's expand the left side of the equation:
[tex]\[
x \times (3x + 4) = 3x^2 + 4x
\][/tex]
So the equation becomes:
[tex]\[
3x^2 + 4x = 112
\][/tex]

5. Select the Correct Option:
Now, looking at the options provided, we see that the correct equation is:
[tex]\[
3x^2 + 4x = 112
\][/tex]
This corresponds to option A.

Thus, the correct answer is option A: [tex]$ 3x^2 + 4x = 112 $[/tex].