High School

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The product of two integers is 112. One number is four more than three times the other.

Which of the following equations 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]

Answer :

Let the first integer be [tex]$x$[/tex] and the second integer be expressed as [tex]$3x+4$[/tex] (since one number is four more than three times the other). Their product is given by

[tex]$$
x(3x+4)=112.
$$[/tex]

Expanding the left side gives

[tex]$$
3x^2+4x=112.
$$[/tex]

This equation matches option A:

[tex]$$
3x^2+4x=112.
$$[/tex]

Thus, the equation that can be used to find one of the numbers is option A.

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