Question

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Which equation represents: "Four times an unknown integer, multiplied by three times the unknown integer plus a different unknown integer, equals 100."
A) 12x^2 + 4xy + 100 = 0
B) 12x^2 − 4xy + 100 = 0
C) 12x^2 + 4xy − 100 = 0
D) 12x^2 − 4xy − 100 = 0

Answer 1

Let's call the first unknown integer x and the second one y.

"Four times an unknown integer"

• We can write it as 4x

"Multiplied by three times the unknown integer plus a different unknown integer"

• 4x is multiplied by 3x+y, so 4x(3x+y)=12x²+4xy

"Equals 100."

• 12x²+4xy=100

And so the answer is C: 12x²+4xy-100=0

Answer 2

12x²+4xy-100=0. The equation that represents the statement of the problem is 12x²+4xy-100=0.

The equation is represents by  "Four times an unknown integer, multiplied by three times the unknown integer plus a different unknown integer, equals 100."

First, we have the statement "four times an unknown integer", this is:

4x

Then, multiplied by three times the unknown integer plus a different unknown integer, that is:

4x(3x+y)

And finally, the equation above is equals to 100.

4x(3x+y)=100

Operating

(4x)(3x)+(4x)(y)=100

12x²+4xy=100

Then,  subtracting 100 on both sides of the equation.

12x²+4xy-100=100-100

Obtaining

12x²+4xy-100=0