Sambuca Juice, Inc. makes donations, pays taxes, and gives employee bonuses from the company's annual income. The donations budget is 5% of the company's income. Taxes represent 12% of the income after deducting donations. The bonus is set to be 14% of the income after deducting both donations and income taxes. The company wants to spend $75,000 on bonuses. How much annual income do they need to generate?

Respuesta :

Let, the companies annual income be x.

Donation budget = 5% of x.

Hence, Donation = [tex]\frac{5}{100} x= \frac{1}{20} x[/tex] ... (1)

Taxes represent 12% after deducting donations.

Hence, taxes is shown as [tex]\frac{12}{100} (x-\frac{x}{20} ) = \frac{12}{100} (\frac{19x}{20} )[/tex] ... (2)

Bonus is 14% after deducting the donations and taxes.

[tex]\frac{14}{100} (x-\frac{12}{100} (\frac{19x}{20} ))[/tex]

Bonus = $ 75000

[tex]75000=\frac{14}{100} (x-\frac{12}{100} (\frac{19x}{20} ))[/tex]

[tex]75000=\frac{14}{100} (x-\frac{228x}{2000} )[/tex]

[tex]75000=\frac{14}{100} (\frac{2000x-228x}{2000} )[/tex]

[tex]75000=\frac{14}{100} (\frac{1772x}{2000} )[/tex]

[tex]75000=\frac{24808x}{200000}[/tex]

x=  $ 604643.66

Annual income of the company is $ 604643.66


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