Answer :
To solve this problem, we need to express the relationship between the two integers algebraically and find an equation that helps us discover one of the numbers.
Let's start by assigning variables to the integers:
- Let the first integer be [tex]\( x \)[/tex].
- According to the problem, the second integer is four more than three times the first integer. Hence, the second integer is [tex]\( 3x + 4 \)[/tex].
Now, we are told that the product of these two integers equals 112. Therefore, we can write the equation:
[tex]\[ x \times (3x + 4) = 112 \][/tex]
Simplifying this equation:
1. Distribute [tex]\( x \)[/tex] across the terms in the parenthesis:
[tex]\[ x \times 3x + x \times 4 = 112 \][/tex]
2. This simplifies to:
[tex]\[ 3x^2 + 4x = 112 \][/tex]
This matches option A, which is [tex]\( 3x^2 + 4x = 112 \)[/tex]. Therefore, the equation that can be used to find one of the numbers is represented by option A.
Let's start by assigning variables to the integers:
- Let the first integer be [tex]\( x \)[/tex].
- According to the problem, the second integer is four more than three times the first integer. Hence, the second integer is [tex]\( 3x + 4 \)[/tex].
Now, we are told that the product of these two integers equals 112. Therefore, we can write the equation:
[tex]\[ x \times (3x + 4) = 112 \][/tex]
Simplifying this equation:
1. Distribute [tex]\( x \)[/tex] across the terms in the parenthesis:
[tex]\[ x \times 3x + x \times 4 = 112 \][/tex]
2. This simplifies to:
[tex]\[ 3x^2 + 4x = 112 \][/tex]
This matches option A, which is [tex]\( 3x^2 + 4x = 112 \)[/tex]. Therefore, the equation that can be used to find one of the numbers is represented by option A.
