Chapter 2, Problem 17RP

Explanation of Solution

Determining a linear equation system:

Assume that the amount $x$ denotes the after-tax profit. It is given that the company earns a profit of $\$60,000$.

Also, it is given that the company pays employees a bonus equal to $5\%$ of after-tax profits. Thus, Bonus is as follows:

$\frac{5}{100}\times x=0.05x$

So, the residue amount after deducting bonus is $=(60000-0.05x)$.

Also, the state tax is $5\%$ of profits after the bonuses are paid.

Thus, the state tax is $=0.05\times (60000-0.05x)$.

So, the residue amount after deducting bonus, state tax is $=60000-\left[0.05\times (60000-0.05x)+(60000-0.05x)\right]$