SOLUTION: Hi there, I had tried to solve this word problems...can't figure it out!! Everytime, I come up with different answers. Any help would be greatly appreciated. Thanks. " At the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Hi there, I had tried to solve this word problems...can't figure it out!! Everytime, I come up with different answers. Any help would be greatly appreciated. Thanks. " At the      Log On


   

Question 334073: Hi there,
I had tried to solve this word problems...can't figure it out!!
Everytime, I come up with different answers. Any help would be greatly appreciated.
Thanks.
" At the end of the year, a business has made a profit of $154,000. They must calculate the amount of tax due to the federal government and to the state. The federal tax rate is 30%, and the state tax rate is 10%. State taxes (ST) are deductible before federal taxes (FT) are calculated, and federal tax are deductible before states taxes are calculated. In other words, state taxes are subtracted from the profits before the 30% federal tax is calculated, and federal taxes are subtracted from the profits before the 10% state tax is calculated. 10% or 30 % of 154,000 does not require a system of equations to solve. Create and solve a system of equations to figure out how much state and federal taxes are owed by this company.

1. Identify the variables first. Do not confuse the tax rate with the amount of tax.
2. Set up a system of two equations. This is the only way that this problem can be solved.
3. Solve the system. Remember to report the answer in dollars."


4. Using the addition (elimination) method to solve systems of equations. Replace the ? with your student number.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the amount of tax paid to the state.

Let represent the amount of tax paid to the federal government.

According to the problem, we start with $154K, subtract the amount paid to the feds and then take 10%, like this:



Likewise, the other equation is set up like this:



This system of equations is set up perfectly to use the substitution method, so take the expression that is equal to in the first equation, and put it in place of in the second equation:



A little arithmetic and a very little algebra gets us to:







rounded to the nearest dollar.

Make the opposite substitution:



You can finish up yourself, I think.

John

My calculator said it, I believe it, that settles it