Chapter 2.1, Problem 37E

To determine

To find: the value of laptop computer.

Answer to Problem 37E

  $\$1500$

Explanation of Solution

Given information:

Benefit from incentive plan for employees who worked for 4 years is equal to sum of $516 and price of laptop computer.

Benefit from incentive plan for employees who worked for 3.5 years is equal to sum of $264 and price of laptop computer.

Calculation:

Let the benefit for incentive plan be x and the price of laptop computer be y.

The equation for the given two statements would be as follows:

  $\begin{array}{l}4x=y+516\mathrm{...}\left(1\right)\\ 3.5x=y+264\mathrm{...}\left(2\right)\end{array}$

Rewrite both the equations in terms of y

  $\begin{array}{l}y=4x-516\mathrm{...}\left[\text{Rewriting equation}\left(1\right)\right]\\ y=3.5x-264\mathrm{...}\left[\text{Rewriting equation}\left(2\right)\right]\end{array}$

Now, equate both the equations and solve them as shown below.

  $\begin{array}{c}4x-516=3.5x-264\\ 4x-3.5x=516-264\\ 0.5x=252\\ x=\frac{252}{0.5}\\ =504\end{array}$

Put the value of x in equation (1) and solve it for y as shown below.

  $\begin{array}{c}y=4\left(504\right)-516\\ =2016-516\\ =1500\end{array}$

Therefore, the value of laptop computer is $1500.