A business has a gross income of $1.32 million. It has promised to pay the CEO a bonus of 20% of net income, which is income after taxes. But the bonus is not subject to taxes because the bonus is an operating expense. The total tax owed is 20% of gross income less the bonus. Our goal is to find the company profit after the bonus and taxes are paid. Let B be the amount on which the bonus is based, and let T be the amount on which taxes are calculated, both in millions of dollars.

(a) Express the taxes paid in terms of the variable T.

(b) The gross income of $1.32 million equals the amount B on which the bonus is based plus the taxes paid. Express this as an equation involving T and B. (Part (a) may be helpful.)

(c) Express the bonus paid in terms of the variable B.

(d) The gross income also equals the amount T on which taxes are based plus the bonus paid. Express this as an equation involving T and B. (Part (c) may be helpful.)

(e) Solve the system of two equations in two unknowns from parts (b) and (d) for the variables T and B.

(f) How much is the bonus?

How much is paid in taxes?

How much profit is left over?