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Answer :
Let's carefully go through the given problem step-by-step to find one of the numbers.
### Problem Statement:
The product of two integers is 112. One number is four more than three times the other.
### Setting up the Equations:
1. Let [tex]\( x \)[/tex] be one of the numbers.
2. The other number then can be written as [tex]\( 3x + 4 \)[/tex], because it is four more than three times [tex]\( x \)[/tex].
### Using the Information:
The product of the two numbers is given as 112. Therefore, we can set up the following equation:
[tex]\[ x \cdot (3x + 4) = 112 \][/tex]
### Simplifying the Equation:
Now, we distribute [tex]\( x \)[/tex] across the term in the parenthesis:
[tex]\[ x \cdot 3x + x \cdot 4 = 112 \][/tex]
[tex]\[ 3x^2 + 4x = 112 \][/tex]
### Formulating the Equation:
We now have the quadratic equation in the form:
[tex]\[ 3x^2 + 4x = 112 \][/tex]
Among the choices given:
- A. [tex]\( 3x^2 + 4x = 112 \)[/tex] aligns with our derived equation.
So, the correct equation that could be used to find one of the numbers is answer choice:
### Answer:
[tex]\[ \boxed{A} \][/tex]
### Problem Statement:
The product of two integers is 112. One number is four more than three times the other.
### Setting up the Equations:
1. Let [tex]\( x \)[/tex] be one of the numbers.
2. The other number then can be written as [tex]\( 3x + 4 \)[/tex], because it is four more than three times [tex]\( x \)[/tex].
### Using the Information:
The product of the two numbers is given as 112. Therefore, we can set up the following equation:
[tex]\[ x \cdot (3x + 4) = 112 \][/tex]
### Simplifying the Equation:
Now, we distribute [tex]\( x \)[/tex] across the term in the parenthesis:
[tex]\[ x \cdot 3x + x \cdot 4 = 112 \][/tex]
[tex]\[ 3x^2 + 4x = 112 \][/tex]
### Formulating the Equation:
We now have the quadratic equation in the form:
[tex]\[ 3x^2 + 4x = 112 \][/tex]
Among the choices given:
- A. [tex]\( 3x^2 + 4x = 112 \)[/tex] aligns with our derived equation.
So, the correct equation that could be used to find one of the numbers is answer choice:
### Answer:
[tex]\[ \boxed{A} \][/tex]
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