Select the correct answer.

The product of two integers is 112. One number is four more than three times the other. Which equation could be used to find one of the numbers?

A. [tex]\(3x^2 + 4x = 112\)[/tex]
B. [tex]\(3x^2 + 4 = 112\)[/tex]
C. [tex]\(4x^2 + 3x = 112\)[/tex]
D. [tex]\(4x^2 + 3 = 112\)[/tex]



Answer :

Alright, let's carefully analyze the problem step-by-step.

1. Let one integer be [tex]\( x \)[/tex].
2. According to the problem, the other number is four more than three times the first number. So the other integer can be represented as [tex]\( 3x + 4 \)[/tex].
3. The product of these two numbers is given to be 112. Therefore, we can write the equation as:
[tex]\[ x \cdot (3x + 4) = 112 \][/tex]
4. Let's simplify this equation:
[tex]\[ x \cdot (3x + 4) = 112 \implies 3x^2 + 4x = 112 \][/tex]
5. Hence, after simplifying the problem, the equation that represents the relationship between the numbers is:
[tex]\[ 3x^2 + 4x = 112 \][/tex]

Therefore, the correct answer is:

A. [tex]\( 3x^2 + 4x = 112 \)[/tex]