# Find B=0.2(100000-T), T=0.4(100000-B) for B, T

#### tarheel2006

104. Bonus and taxes. 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. 106. Free market. The equations S = 5000 + 200x and D = 9500 - 100x express the supply S and the demand D, respectively, for a popular compact disc brand in terms of its price x (in dollars). a) Graph the equations on the same coordinate system. b) What happens to the supply as the price increases? c) What happens to the demand as the price increases? d) The price at which supply and demand are equal is called the equilibrium price.What is the equilibrium price? #### Subhotosh Khan ##### Super Moderator Staff member Re: i need help with 2 word problems tarheel2006 said: 104. Bonus and taxes. 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. Where is the graph??
b) Solve the system algebraically to find the bonus and
the amount of tax.

The equations for T and B gives you two equations with two unknowns.

If you don't know how to tackle such problems, please go to:

http://www.purplemath.com/modules/systlin1.htm

106. Free market. The equations S = 5000 + 200x and
D = 9500 - 100x express the supply S and the
demand D, respectively, for a popular compact disc brand
in terms of its price x (in dollars).
a) Graph the equations on the same coordinate system.
b) What happens to the supply as the price increases?
c) What happens to the demand as the price increases?
d) The price at which supply and demand are equal is
called the equilibrium price.What is the equilibrium
price?

What is the definition of equilibrium price?

How can you use that definition for the given problem?

#### tarheel2006

##### New member
Re: i need help with 2 word problems

i have tried to copy the graph from the pdf file but i can't get it and i have not done any work b/c i don't know how to set up the problems. I am still trying to attach the graph to a posting.

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: i need help with 2 word problems

tarheel2006 said:
i have tried to copy the graph from the pdf file but i can't get it and i have not done any work b/c i don't know how to set up the problems. I am still trying to attach the graph to a posting.
For the first problem - part (b) - there is nothing to set-up.

You are given two equations with two unknowns - solve it.

#### tarheel2006

##### New member
Re: i need help with 2 word problems

So for the first word problem I have 3 equations?

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: i need help with 2 word problems

tarheel2006 said:
So for the first word problem I have 3 equations?
B = 0.20(100,000 - T ).................................................................(1)

T =0.40(100,000 - B)...................................................................(2)

unknowns T & B

Where is the third equation (or third unknown) coming from??

#### tarheel2006

##### New member
Re: i need help with 2 word problems

Thank you for the help ont he first one.b) Solve the system algebraically to find the bonus and
the amount of tax.
T=28292.68
B=29268.30

I hope i did it right. the def. of eqil. prince for Question 106 I assume from the question is: The price at which supply and demand are equal is
called the equilibrium price.

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: i need help with 2 word problems

tarheel2006 said:
Thank you for the help ont he first one.b) Solve the system algebraically to find the bonus and
the amount of tax.
T=28292.68
B=29268.30

You can check your answer by putting these values back into the equations - and check if the equality holds true.

incorrect.

I hope i did it right. the def. of eqil. prince for Question 106 I assume from the question is: The price at which supply and demand are equal is called the equilibrium price.

Now tell us how can you use the definition above - with the information given in your problem - solve 2(d).

2(a),(b) and (c) are essay questions - your textbook should have explanations regarding these.

#### tarheel2006

##### New member
Re: i need help with 2 word problems

So in problem 104 where did i go wrong? I sustituted the for the variable witht he equation
B = 0.20(100,000 - T )
=.20*100000-.20*T
=20000-.20(0.40(100,000 - B))
=20000-8000-.08b
=12000-.08b???

#### Denis

##### Senior Member
Re: i need help with 2 word problems

Methinks you better talk to your teacher, tarheel.

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: i need help with 2 word problems

tarheel2006 said:
So in problem 104 where did i go wrong? I sustituted the for the variable witht he equation
B = 0.20(100,000 - T )
=.20*100000-.20*T
=20000-.20(0.40(100,000 - B))
=20000-8000 + .08B
=12000 + .08B

Correct upto here - Now solve for B

???