Chapter 6.3, Problem 30PPS

a.

To determine

To find the height of the statue

Answer to Problem 30PPS

15.6 feet

Explanation of Solution

Given:

Height of an office building: b

Height of the granite statue: g

Total height of the building and the statue: 326.6 feet

Difference in heights between the building and the statue: 295.4 feet

Calculation:

Let b be the height of the building and g be the height of the granite statue.

The total height of the building and the statue can be represented by the equation:

  $b+g=326.6\to \text{(1)}$

The difference in heights of the building and the statue can be represented by the equation:

  $b-g=295.4\to \text{(2)}$

To find the height of the statue use elimination method as follows:

Subtract equation (2) from equation (1), so that b can be eliminated.

  $\begin{array}{l}b+g=326.6\\ \frac{-b+g=-295.4}{2g=31.2}\text{ [When subtracting the sign of equation (2) changes]}\end{array}$

  $\begin{array}{l}\Rightarrow 2g=31.2\\ \Rightarrow g=\frac{31.2}{2}\\ \Rightarrow g=15.6\end{array}$

Conclusion:

Therefore, the granite statue is 15.6 feet tall.

b.

To determine

To find the height of the building

Answer to Problem 30PPS

311 feet

Explanation of Solution

Given:

Height of an office building: b

Height of the granite statue: g

Total height of the building and the statue: 326.6 feet

Difference in heights between the building and the statue: 295.4 feet

From subpart (a), the height of the granite statue is 15.6 feet.

Calculation:

Let b be the height of the building and g be the height of the granite statue.

The total height of the building and the granite statue is 326.6 feet, which can be represented as follows:

  $b+g=326.6\to \text{(1)}$

Substitute the height of the granite statue $g=15.6$ in equation (1).

  $\begin{array}{c}b+15.6=326.6\text{ [Subtract 15}\text{.6 on both sides]}\\ b=326.6-15.6\\ b=311\end{array}$

Conclusion:

Therefore, the building is 311 feet tall.