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Answer :
To solve the problem, we need to find an equation in terms of one of the integers.
1. Define Variables:
- Let one of the integers be [tex]\( x \)[/tex].
2. Express the Second Integer:
- We are told that the second integer is four more than three times the first integer. So, the second integer can be expressed as [tex]\( 3x + 4 \)[/tex].
3. Set Up the Product Equation:
- We know that the product of these two integers is 112. So, we can write:
[tex]\[
x \cdot (3x + 4) = 112
\][/tex]
4. Expand the Equation:
- Distribute [tex]\( x \)[/tex] in the equation:
[tex]\[
x \cdot 3x + x \cdot 4 = 112
\][/tex]
[tex]\[
3x^2 + 4x = 112
\][/tex]
5. Identify the Correct Equation:
- Looking at the expanded equation, [tex]\( 3x^2 + 4x = 112 \)[/tex], we see that this matches option A.
Therefore, the correct answer is A. [tex]\(3x^2 + 4x = 112\)[/tex].
1. Define Variables:
- Let one of the integers be [tex]\( x \)[/tex].
2. Express the Second Integer:
- We are told that the second integer is four more than three times the first integer. So, the second integer can be expressed as [tex]\( 3x + 4 \)[/tex].
3. Set Up the Product Equation:
- We know that the product of these two integers is 112. So, we can write:
[tex]\[
x \cdot (3x + 4) = 112
\][/tex]
4. Expand the Equation:
- Distribute [tex]\( x \)[/tex] in the equation:
[tex]\[
x \cdot 3x + x \cdot 4 = 112
\][/tex]
[tex]\[
3x^2 + 4x = 112
\][/tex]
5. Identify the Correct Equation:
- Looking at the expanded equation, [tex]\( 3x^2 + 4x = 112 \)[/tex], we see that this matches option A.
Therefore, the correct answer is A. [tex]\(3x^2 + 4x = 112\)[/tex].
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