Answer :
To solve the problem, we need to find an equation that helps us determine one of the numbers that fits the given conditions:
1. Product of two integers is 112: Let's call one of the integers [tex]\( x \)[/tex]. Therefore, the product is given by multiplying this number with another integer.
2. One number is four more than three times the other: If we let [tex]\( x \)[/tex] be one of the numbers, then the other number would be [tex]\( 3x + 4 \)[/tex].
Now let's form the equation based on these conditions:
- The product of [tex]\( x \)[/tex] and [tex]\( 3x + 4 \)[/tex] must equal 112.
So, we set up the equation:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
- Expanding the equation:
[tex]\[
3x^2 + 4x = 112
\][/tex]
The equation that matches this expanded form is:
- Option A: [tex]\( 3x^2 + 4x = 112 \)[/tex]
This is the correct equation to use for finding one of the numbers based on the given conditions.
1. Product of two integers is 112: Let's call one of the integers [tex]\( x \)[/tex]. Therefore, the product is given by multiplying this number with another integer.
2. One number is four more than three times the other: If we let [tex]\( x \)[/tex] be one of the numbers, then the other number would be [tex]\( 3x + 4 \)[/tex].
Now let's form the equation based on these conditions:
- The product of [tex]\( x \)[/tex] and [tex]\( 3x + 4 \)[/tex] must equal 112.
So, we set up the equation:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
- Expanding the equation:
[tex]\[
3x^2 + 4x = 112
\][/tex]
The equation that matches this expanded form is:
- Option A: [tex]\( 3x^2 + 4x = 112 \)[/tex]
This is the correct equation to use for finding one of the numbers based on the given conditions.
