SOLUTION: 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.

Question 295619: 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)
solve the system algebraically to find the bonus and the amount of tax
Found 2 solutions by richwmiller, palanisamy:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!

B=0.20(100,000-T)
T=0.40(100,000-B)
solve for b
t=.4*100000-.4b
t-.4*100000=-.4b
.4*100000-t=.4b
(.4*100000-t)/.4=b
100000-t/.4=b
b=.2*(100000-t)
b=.2*100000-.2t
set them equal
.2*100000-.2t=100000-t/.4
t=34782.6
b=.2*100000-.2t
b=13043.5, t=34782.6
or
B = 20000.-0.2T
T = 40000.-0.4B
B=13043.5, T=34782.6
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
The given equations are
B=0.20(100,000-T) ...(1)
and T=0.40(100,000-B)
T = 400000-0.40B ...(2)

Put B = 0.20(100,000-T) in (2)
T=400000-(0.20(100,000-T)
T= 400000-20000+0.20T
T-0.20T = 200000
0.8T=200000
T=200000/(0.8)
T=2500000
(1)=> B= 200000-(0.20)*2500000
B=200000-50000
B=150000

RELATED QUESTIONS
A company has an income of $100,000 before paying taxes and a bonus. The bonus B is to be (answered by stanbon)
Please Help! I have no idea where to start. A company has an income of $100,000... (answered by dabanfield)
A company has income of $100,000 before paying taxes and a bouns. The bouns B is to be... (answered by rapaljer)
A company has an income of $100,000 before paying taxes and a bonus. The bonus B is to be (answered by richwmiller)
A study of 200 grocery chains revealed these incomes after taxes: Income after... (answered by ewatrrr)
When calculating his income tax an accountant realized that his federal tax was 30% of... (answered by Theo)
hen calculating his income tax an accountant realized that his federal tax was 40% of his (answered by ikleyn)
an engineering firm earns a monthly salary of $3457 and an annual bonus that is 16.3% of... (answered by robertb)
It's a Microeconomic question related to choice under uncertainty: Kate will earn... (answered by Alan3354)