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Answer :
Sure, let's solve this step-by-step!
We are given two pieces of information about the integers:
1. The product of the two integers is 112.
2. One number is four more than three times the other.
Let's set up our variables:
- Let [tex]\( x \)[/tex] be one of the integers.
- Let [tex]\( y \)[/tex] be the other integer.
From the problem statement, we know:
[tex]\[ x \cdot y = 112 \][/tex]
We also know that one number is four more than three times the other:
[tex]\[ y = 3x + 4 \][/tex]
Now, we can substitute [tex]\( y \)[/tex] in the first equation using the expression we have for [tex]\( y \)[/tex]:
[tex]\[ x \cdot (3x + 4) = 112 \][/tex]
Expanding and simplifying, we get:
[tex]\[ 3x^2 + 4x = 112 \][/tex]
This is the equation we can use to find one of the numbers.
So the correct answer is:
[tex]\[ \text{A. } 3x^2 + 4x = 112 \][/tex]
We are given two pieces of information about the integers:
1. The product of the two integers is 112.
2. One number is four more than three times the other.
Let's set up our variables:
- Let [tex]\( x \)[/tex] be one of the integers.
- Let [tex]\( y \)[/tex] be the other integer.
From the problem statement, we know:
[tex]\[ x \cdot y = 112 \][/tex]
We also know that one number is four more than three times the other:
[tex]\[ y = 3x + 4 \][/tex]
Now, we can substitute [tex]\( y \)[/tex] in the first equation using the expression we have for [tex]\( y \)[/tex]:
[tex]\[ x \cdot (3x + 4) = 112 \][/tex]
Expanding and simplifying, we get:
[tex]\[ 3x^2 + 4x = 112 \][/tex]
This is the equation we can use to find one of the numbers.
So the correct answer is:
[tex]\[ \text{A. } 3x^2 + 4x = 112 \][/tex]
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