help solve this math problem?

Question

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 deductable 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.

Answer 1

Rewrite these equations as

B+0.2T=20,000
0.4B+T=40,000

Multiply the second equation by 5/2:

B+0.2T=20,000
B+2.5T=100,000

Subtract the first equation from the second:

2.3T=80,000

so T = 80,000/2.3 = $34,782.61.

That means B = 20,000-0.2*T = $13,043.48.

Answer 2

B= 0.20(100,000 -T)

can be written as B + 0.2T = 20,000


similarly,

T = 0.40(100,000 -B)

can be written as 0.4B + T = 40,000


multiply equ (1) by 10 and equ(2) by 2 then


10B + 2T = 200,000
0.8B + 2T = 80,000

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9.2B= 120,000

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Bonus = 120,000/9.2


Bonus= 13,043.48

By putting the Bonus in the above formula


Tax= 34,782.61