# Thread: Bonus and taxes: graphing

1. ## Bonus and taxes: graphing

Here is the one with the graph I tried to post earlier. The graph should be showing up now.

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.

I started down the path of trying to solve B=0.20(100000-T) and T=0.40(100000-B) as B=20000-0.20T and T=40000-0.40B, then quickly realized this was not correct at all.

Any direction you could provide would be much appreciated. Thank you.

2. I'm still totally lost on this one. I only have this question and one other to answer this week in school.

If anyone feels up to the task of helping me out, I won't turn you down.

3. My assumption is I need to somehow get the x,y values off the graph for B and T, but I cannot figure out or remember how to do that.

4. Use substitution. In your first post, both of your equations for B and for T are correct. So in the first equation, replace the "T" with 0.4(100,000 - B).

That will let the re-expressed first equation lead you to the solution for B. You can then easily determine T.

Be sure to check that your proposed B and T satisfy the original problem. You'll also see that your calculated B and T do appear to agree with the intersection of the two lines in the graph.

5. Originally Posted by LochWulf
Use substitution. In your first post, both of your equations for B and for T are correct. So in the first equation, replace the "T" with 0.4(100,000 - B).

That will let the re-expressed first equation lead you to the solution for B. You can then easily determine T.

Be sure to check that your proposed B and T satisfy the original problem. You'll also see that your calculated B and T do appear to agree with the intersection of the two lines in the graph.
Many thanks!

6. Glad it helped, DK.