High School

A construction company is analyzing which of its older projects need renovation. Building B was built two years before building C. Building D was built two years before building B. The product of building B's age and building D's age is at least 195.

If [tex]x[/tex] represents the age of building C, which inequality represents this situation?

A) [tex]x^2 + 6x + 8 \geq 195[/tex]
B) [tex]x^2 + 4x + 4 \geq 195[/tex]
C) [tex]x^2 + 8x + 16 \geq 195[/tex]
D) [tex]x^2 + 4 \geq 195[/tex]

Answer :

Final answer:

The correct inequality is x^2 + 6x + 8 ≥ 195.

Explanation:

The inequality that represents the situation is x^2 + 6x + 8 ≥ 195.

To determine the correct inequality, we need to analyze the information given. Building B was built two years before building C, and building D was built two years before building B. This means that the age of building C is equal to the age of building B plus 2, and the age of building D is equal to the age of building B plus 4.

The product of building B's age (x) and building D's age (x+4) is at least 195, so we have the inequality x(x+4) ≥ 195. Expanding the quadratic equation, we get x^2 + 4x ≥ 195. Rearranging the terms, we obtain x^2 + 6x + 8 ≥ 195.

Learn more about Inequalities here:

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