A ccompany has an income of $100,000 before paying taxes and abonus. The bonus B

Question

A ccompany has an income of $100,000 before paying taxes and abonus. The bonus B is to be 20% of the income afterdeducting income taxes T but before deducting the bonus.So B = 0.20 (100,000 - T). Because the bonus is adeductible 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 systems algebraically to find the bonus and theamount of tax. T = 0.40(100,000 -B) B= 0.20(100,000 - T) A ccompany has an income of $100,000 before paying taxes and abonus. The bonus B is to be 20% of the income afterdeducting income taxes T but before deducting the bonus.So B = 0.20 (100,000 - T). Because the bonus is adeductible 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 systems algebraically to find the bonus and theamount of tax. T = 0.40(100,000 -B) B= 0.20(100,000 - T)

Explanation / Answer

all you need to do is plug in one equation into theother T=0.40(100,000-B) B=0.20(100,000-T) solve for one T=0.40(100,000-(0.20(100,000-T))) distribute and add like terms T=40,000-.040(20,000-0.20T) T=40,000-8,000+.080t T-.080T=40,000-8,000+.080T-.080T 0.92T=32,000 T=34,782.6087 solve for B using T B=0.20(100,000-T) multiply and solve for B B=0.20(100,000-34,782.6087) B=0.20(65,217.3913) B=13,043.47826

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