Answer :
To solve this problem, we need to set up an equation based on the conditions given:
1. Let [tex]\( x \)[/tex] be one of the integers.
2. Then, the other integer, according to the problem, would be [tex]\( 3x + 4 \)[/tex] because it is four more than three times the first integer.
The problem also states that the product of these two integers is 112. This can be expressed as:
[tex]\[ x \times (3x + 4) = 112 \][/tex]
Now, let's simplify and solve this equation:
- Distribute [tex]\( x \)[/tex] in the equation:
[tex]\[
x \cdot (3x + 4) = 3x^2 + 4x
\][/tex]
- Set the expression equal to 112:
[tex]\[
3x^2 + 4x = 112
\][/tex]
The equation [tex]\( 3x^2 + 4x = 112 \)[/tex] matches with option A. Therefore, the equation that could be used to find one of the numbers is:
A. [tex]\( 3x^2 + 4x = 112 \)[/tex]
This equation reflects the relationship described in the problem and can be solved to find the value of [tex]\( x \)[/tex].
1. Let [tex]\( x \)[/tex] be one of the integers.
2. Then, the other integer, according to the problem, would be [tex]\( 3x + 4 \)[/tex] because it is four more than three times the first integer.
The problem also states that the product of these two integers is 112. This can be expressed as:
[tex]\[ x \times (3x + 4) = 112 \][/tex]
Now, let's simplify and solve this equation:
- Distribute [tex]\( x \)[/tex] in the equation:
[tex]\[
x \cdot (3x + 4) = 3x^2 + 4x
\][/tex]
- Set the expression equal to 112:
[tex]\[
3x^2 + 4x = 112
\][/tex]
The equation [tex]\( 3x^2 + 4x = 112 \)[/tex] matches with option A. Therefore, the equation that could be used to find one of the numbers is:
A. [tex]\( 3x^2 + 4x = 112 \)[/tex]
This equation reflects the relationship described in the problem and can be solved to find the value of [tex]\( x \)[/tex].
