Chapter 8, Problem 2PSP

To determine

To find:

After how many years are the total costs of the two refrigerators the same?

Answer to Problem 2PSP

There is no solution for the given problem.

Explanation of Solution

Given:

Refrigerator A has a price of $600 and costs $35 per year in the electricity to operate. Refrigerator B has a price of $800 and costs $40 per year in electricity to operate.

Calculation:

Let x represent number of years and y represent total cost.

We have been given that refrigerator A costs $35 per year in the electricity to operate, so operating cost of electricity after x years would be $35x$ . The total cost of operating refrigerator A would be price of refrigerator plus electricity cost. We can represent this information in an equation as:

  $y=35x+600$

We have been given that refrigerator B costs $40 per year in the electricity to operate, so operating cost of electricity after x years would be $40x$ . The total cost of operating refrigerator B would be price of refrigerator plus electricity cost. We can represent this information in an equation as:

  $y=40x+800$

Now we will solve for x by equating both equations as:

  $\begin{array}{l}40x+800=35x+600\\ 40x-35x+800=35x-35x+600\\ 5x+800=600\\ 5x+800-800=600-800\\ 5x=-200\\ \frac{5x}{5}=-\frac{200}{5}\\ x=-40\end{array}$

Since time cannot negative, therefore, there is no solution for the given problem.