Question

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 x represents the age of Building C, which of the following represents this situation?

Answer 1

The situation can be represented by the inequality x ≥ 22.31.

Step-by-step explanation:

The situation described in the question can be represented as follows:

Building B = x - 2
Building C = x
Building D = x - 4

The product of Building B's age and Building D's age is at least 195, so we have (x - 2)(x - 4) ≥ 195.

To solve this inequality, we need to find the values of x that satisfy it. We can start by expanding the equation: x^2 - 6x + 8 ≥ 195.

By rearranging the terms, we get x^2 - 6x - 187 ≥ 0.

Using factoring or the quadratic formula, we find that the roots of this equation are approximately -16.31 and 22.31. Since we're dealing with ages of buildings, we can disregard the negative root. Therefore, the valid range for x is x ≥ 22.31.

So, the situation can be represented by the inequality x ≥ 22.31.

Answer 2

you need to make an equation for each of the buildings age.

C = x
B = x + 2
D = B + 2 which is (x + 2) + 2 so x + 4

Product means to multiple so (B)(D) which is (x + 2)(x+4)