Answer :
To solve this problem, we need to set up an equation based on the given conditions.
1. Identify the variables:
- Let one of the integers be [tex]\( x \)[/tex].
- According to the problem, the other integer is "four more than three times the other." This can be expressed as [tex]\( 3x + 4 \)[/tex].
2. Set up the product equation:
- The product of the two integers is 112. So, we can write:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
3. Simplify the equation:
- Distribute the [tex]\( x \)[/tex] across the term [tex]\( (3x + 4) \)[/tex]:
[tex]\[
3x^2 + 4x = 112
\][/tex]
4. Choose the correct answer:
- Looking at the options, the equation [tex]\( 3x^2 + 4x = 112 \)[/tex] corresponds to option A.
Thus, the correct equation to find one of the numbers is [tex]\( 3x^2 + 4x = 112 \)[/tex], which matches option A.
1. Identify the variables:
- Let one of the integers be [tex]\( x \)[/tex].
- According to the problem, the other integer is "four more than three times the other." This can be expressed as [tex]\( 3x + 4 \)[/tex].
2. Set up the product equation:
- The product of the two integers is 112. So, we can write:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
3. Simplify the equation:
- Distribute the [tex]\( x \)[/tex] across the term [tex]\( (3x + 4) \)[/tex]:
[tex]\[
3x^2 + 4x = 112
\][/tex]
4. Choose the correct answer:
- Looking at the options, the equation [tex]\( 3x^2 + 4x = 112 \)[/tex] corresponds to option A.
Thus, the correct equation to find one of the numbers is [tex]\( 3x^2 + 4x = 112 \)[/tex], which matches option A.
