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.
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.
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.