Answer :
To solve this problem, we're trying to find which equation represents the given situation. Here's a step-by-step explanation:
1. Understand the Problem: We are told that the product of two integers is 112 and that one number is four more than three times the other number.
2. Define the Variables: Let's call the first number [tex]\( x \)[/tex]. According to the problem, the second number would then be "four more than three times the other number," which can be expressed as [tex]\( 3x + 4 \)[/tex].
3. Set Up the Equation: The product of these two numbers should equal 112. Therefore, we can write the equation as:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
4. Simplify the Equation: Distribute [tex]\( x \)[/tex] in the equation:
[tex]\[
3x^2 + 4x = 112
\][/tex]
5. Identify the Correct Option: Now, let's compare the simplified equation with the given options. The equation [tex]\( 3x^2 + 4x = 112 \)[/tex] matches option A.
Therefore, the correct equation that could be used to find one of the numbers is:
A. [tex]\( 3x^2 + 4x = 112 \)[/tex]
1. Understand the Problem: We are told that the product of two integers is 112 and that one number is four more than three times the other number.
2. Define the Variables: Let's call the first number [tex]\( x \)[/tex]. According to the problem, the second number would then be "four more than three times the other number," which can be expressed as [tex]\( 3x + 4 \)[/tex].
3. Set Up the Equation: The product of these two numbers should equal 112. Therefore, we can write the equation as:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
4. Simplify the Equation: Distribute [tex]\( x \)[/tex] in the equation:
[tex]\[
3x^2 + 4x = 112
\][/tex]
5. Identify the Correct Option: Now, let's compare the simplified equation with the given options. The equation [tex]\( 3x^2 + 4x = 112 \)[/tex] matches option A.
Therefore, the correct equation that could be used to find one of the numbers is:
A. [tex]\( 3x^2 + 4x = 112 \)[/tex]
