Chapter 3, Problem 17MCQ

Solution

(a)

To find: The solution of the system.

The solution of the system is equal to $\left(4,871\right)$ .

Given information:

An ordinary refrigerator costs $\$503$ and has an estimated annual operating cost of $\$92$ . An energy efficient model cost $\$615$ with an estimated annual operating cost of $\$64$ .

Calculation:

Let $x$ be the number of years.

Let $y$ be the total cost of the refrigerator.

An ordinary refrigerator costs $\$503$ and has an estimated annual operating cost of $\$92$ .

It can be represented in equation below:

  $y=92x+503\mathrm{...}\left(1\right)$

An energy efficient model cost $\$615$ with an estimated annual operating cost of $\$64$ .

It can be represented in equation below:

  $y=64x+615\mathrm{...}\left(2\right)$

Solve the equation (1) and (2).

Substitute the value of $y$ from equation (2) in the equation (1) and solve for $x$ :

  $\begin{array}{c}64x+615=92x+503\\ 92x-64x=615-503\\ 28x=112\\ x=4\end{array}$

Substitute $x=4$ in the equation (1) and calculate the value of $y$ :

  $\begin{array}{c}y=92\left(4\right)+503\\ =368+503\\ =871\end{array}$

Therefore, the solution of the system is $\left(4,871\right)$ .

(b)

To find: The meaning of the solution of the system.

After $4$ years the total cost of the refrigerator will be $\$871$ .

Given information:

An ordinary refrigerator costs $\$503$ and has an estimated annual operating cost of $\$92$ . An energy efficient model cost $\$615$ with an estimated annual operating cost of $\$64$ .

Calculation:

Let $x$ be the number of years.

Let $y$ be the total cost of the refrigerator.

From part (a) and (b),

  $x=4,y=871$

It means that after four years the total cost of the refrigerator will be $\$871$ .