Chapter 9.7, Problem 22P

To determine

To solve: the system of equations in two variables.

Answer to Problem 22P

The year in which Lincoln memorial was built was 1922 and Jefferson memorial was built in 1943.

Explanation of Solution

Given information:

In 1985, the Lincoln Memorial was $1\frac{1}{2}$ times as old as the Jefferson Memorial. If the Lincoln Memorial was built 21 years before the Jefferson Memorial.

Formula used:

Age problem.

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

Step2. Let b = the Lincoln’s Memorial age .

Let c = the Jefferson‘s Memorial age .

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

Step4. Solve the equations.

Calculation:

Consider ,

Let b = the Lincoln’s Memorial age in 1985.

Let c = the Jefferson’s Memorial age in 1985.

According to the equation,

  $\begin{array}{l}=b=1\frac{1}{2}c\\ =b=\frac{3}{2}c\\ =b=1.5c\text{ (i)}\end{array}$

Also,

  $=b=c+21\text{ (ii)}$

Equating equation (i) in (ii)

  $\begin{array}{l}=1.5c=c+21\\ =1.5c-c=21\\ =\frac{0.5c}{0.5}=\frac{21}{0.5}\\ =c=42\end{array}$

Substituting value of c in (ii) we have,

  $\begin{array}{l}=b=42+21\\ =b=63\end{array}$

Hence, the year in which Lincoln memorial was built

  $1985-63=1922$ .

The year in which Jefferson memorial was built

  $1985-42=1943$ .

The year in which Lincoln memorial was built was 1922 and Jefferson memorial was built in 1943.