Question 304126: Please Help! I have no idea where to start.
A company has an income of $100,000
before paying taxes and a bonus. The bonus B is to be
20% of the income after deducting income taxes T but
before deducting the bonus. So
B = 0.20(100,000 - T ).
Because the bonus is a deductible expense, the amount of
income tax T at a 40% rate is 40% of the income after
deducting the bonus. So
T = 0.40(100,000 - B).
a) Use the accompanying graph to estimate the values of
T and B that satisfy both equations.
b) Solve the system algebraically to find the bonus and
the amount of tax.
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! 1.) B = 0.20(100,000 - T )
2.) T = 0.40(100,000 - B)
You have two equations in two unknowns to solve simultaneously.
Rewrite 1.) as
3.) B = 20000 - .2*T
and 2.) as
4.) T = 40000 - .4*B
Substitute (20000 - .2*T) from 3.) in 4.) and solve for T:
T = 40000 - .4*(20000 - .2*T)
T = 40000 - 8000 + .08*T
T - .08*T = 32000
.92*T = 3200
T = 3200/.92
T = ?
Take the value for T above and substitute in 3.) to calculate B.
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