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Answer :
Let's solve the problem step-by-step:
1. Understand the Problem: We are given that the product of two integers is 112. Also, one number is four more than three times the other number.
2. Define the Variables:
- Let [tex]\( x \)[/tex] be the first number.
- Then the second number would be [tex]\( 3x + 4 \)[/tex] since it is four more than three times the first number.
3. Set up the Equation: The product of the two numbers is given as 112. Therefore, we can write the equation:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
4. Simplify the Equation: Expand the equation:
[tex]\[
x \cdot 3x + x \cdot 4 = 112
\][/tex]
This simplifies to:
[tex]\[
3x^2 + 4x = 112
\][/tex]
5. Identify the Correct Option: The equation [tex]\( 3x^2 + 4x = 112 \)[/tex] matches with option A.
Therefore, the correct equation to solve for one of the numbers is option A. [tex]\( 3x^2 + 4x = 112 \)[/tex].
1. Understand the Problem: We are given that the product of two integers is 112. Also, one number is four more than three times the other number.
2. Define the Variables:
- Let [tex]\( x \)[/tex] be the first number.
- Then the second number would be [tex]\( 3x + 4 \)[/tex] since it is four more than three times the first number.
3. Set up the Equation: The product of the two numbers is given as 112. Therefore, we can write the equation:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
4. Simplify the Equation: Expand the equation:
[tex]\[
x \cdot 3x + x \cdot 4 = 112
\][/tex]
This simplifies to:
[tex]\[
3x^2 + 4x = 112
\][/tex]
5. Identify the Correct Option: The equation [tex]\( 3x^2 + 4x = 112 \)[/tex] matches with option A.
Therefore, the correct equation to solve for one of the numbers is option A. [tex]\( 3x^2 + 4x = 112 \)[/tex].
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