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The product of two integers is 112. One number is four more than three times the other. Which equation could be used to find one of the numbers?

A. [tex]\(3x^2 + 4x = 112\)[/tex]
B. [tex]\(3x^2 + 4 = 112\)[/tex]
C. [tex]\(4x^2 + 3x = 112\)[/tex]
D. [tex]\(4x^2 + 3 = 112\)[/tex]

Sagot :

GinnyAnswer
Alright, let's carefully analyze the problem step-by-step.

1. Let one integer be [tex]\( x \)[/tex].
2. According to the problem, the other number is four more than three times the first number. So the other integer can be represented as [tex]\( 3x + 4 \)[/tex].
3. The product of these two numbers is given to be 112. Therefore, we can write the equation as:
[tex]\[ x \cdot (3x + 4) = 112 \][/tex]
4. Let's simplify this equation:
[tex]\[ x \cdot (3x + 4) = 112 \implies 3x^2 + 4x = 112 \][/tex]
5. Hence, after simplifying the problem, the equation that represents the relationship between the numbers is:
[tex]\[ 3x^2 + 4x = 112 \][/tex]

Therefore, the correct answer is:

A. [tex]\( 3x^2 + 4x = 112 \)[/tex]
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