Chapter 9.7, Problem 21P

To determine

To solve: the system of equations in two variables.

Answer to Problem 21P

The Brooklyn Bridge was built in $1883$ .

The Golden Gate Bridge was built in $1937$ .

Explanation of Solution

Given information:

The Golden Gate Bridge was completed 54 years after Brooklyn Bridge was. In 1983, The Golden Gate Bridge was $\frac{23}{50}$ as old as the Brooklyn Bridge.

Formula used:

Age problem.

Step1. The problem asks for the Bob’s age and Claire’s age now.

Step2. Let b = the Brooklyn Bridge’s age .

Let c = the Golden Gate Bridge‘s age .

Step3. Use the facts of the problem to write two equations.

Step4. Solve the equations.

Calculation:

Consider ,

Let b = the Brooklyn Bridge’s age .

Let c = the Golden Gate Bridge’s age .

According to the equation,

  $=c=(b-54)\text{ (i)}$

Also,

  $=c=\frac{23}{50}\text{b (ii)}$

Equating equation (i) in (ii)

  $\begin{array}{l}=b-54=\frac{23}{50}b\\ =50(b-54)=23b\\ =50b-2700=23b\\ =50b-23b=2700\\ =\frac{27b}{27}=\frac{2700}{27}\\ =b=100\end{array}$

Hence, the Brooklyn Bridge was built in $1983-100=1883$ .

The Golden Gate Bridge was built in $1883+54=1937$