Answer :
Sure! Let's break down the problem step by step to find the correct equation you can use to solve for one of the numbers.
1. Understanding the Problem:
- We are given that the product of two integers is 112.
- One of the numbers is four more than three times the other number.
2. Define the Variables:
- Let's call the first integer [tex]\( x \)[/tex].
- According to the problem, the second integer would then be [tex]\( 3x + 4 \)[/tex] (since it is four more than three times [tex]\( x \)[/tex]).
3. Set Up the Equation:
- Since the product of the two integers is 112, we can write the equation as:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
4. Simplify the Equation:
- Distribute [tex]\( x \)[/tex] to get:
[tex]\[
3x^2 + 4x = 112
\][/tex]
This corresponds to the equation shown in option A: [tex]\( 3x^2 + 4x = 112 \)[/tex].
So, the correct equation that could be used to find one of the numbers is option A: [tex]\( 3x^2 + 4x = 112 \)[/tex].
1. Understanding the Problem:
- We are given that the product of two integers is 112.
- One of the numbers is four more than three times the other number.
2. Define the Variables:
- Let's call the first integer [tex]\( x \)[/tex].
- According to the problem, the second integer would then be [tex]\( 3x + 4 \)[/tex] (since it is four more than three times [tex]\( x \)[/tex]).
3. Set Up the Equation:
- Since the product of the two integers is 112, we can write the equation as:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
4. Simplify the Equation:
- Distribute [tex]\( x \)[/tex] to get:
[tex]\[
3x^2 + 4x = 112
\][/tex]
This corresponds to the equation shown in option A: [tex]\( 3x^2 + 4x = 112 \)[/tex].
So, the correct equation that could be used to find one of the numbers is option A: [tex]\( 3x^2 + 4x = 112 \)[/tex].
