A business has a gross income of $1.14 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.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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A Büsiness has a gross income of $1.14 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.
.2T
(b) The gross income of $1.14 million equals the amount B on which the bonus is based plus the taxes paid. Express this as an equation involving T and 8. (Part (a) may be helpful.)
1.14 = B+ .2T
(c) Express the bonus paid in terms of the variable B.
.2B
(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.)
1.14 = T+ .2B
(e) Solve the system of two equations in two unknowns from parts (b) and (d) for the variables T and B.
T = 114
B =
(f) How much is the bonus?
%24
million
How much is paid in taxes?
24
million
Transcribed Image Text:A Büsiness has a gross income of $1.14 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. .2T (b) The gross income of $1.14 million equals the amount B on which the bonus is based plus the taxes paid. Express this as an equation involving T and 8. (Part (a) may be helpful.) 1.14 = B+ .2T (c) Express the bonus paid in terms of the variable B. .2B (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.) 1.14 = T+ .2B (e) Solve the system of two equations in two unknowns from parts (b) and (d) for the variables T and B. T = 114 B = (f) How much is the bonus? %24 million How much is paid in taxes? 24 million
T= 1.14
B 3=
(f) How much is the bonus?
million
How much is paid in taxes?
%$4
million
How much profit is left over?
million
Need Help?
Read It
Transcribed Image Text:T= 1.14 B 3= (f) How much is the bonus? million How much is paid in taxes? %$4 million How much profit is left over? million Need Help? Read It
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