# Bonus

Gross wage was 527 EUR including 16% bonus.

How many EUR were bonuses?

Result

b =  72.69 EUR

#### Solution:

$\ \\ a + 16/100 \ a = 527 \ \\ \ \\ 116a = 52700 \ \\ \ \\ a = \dfrac{ 13175 }{ 29 } \doteq 454.310345 \ \\ \ \\ b = 527 - a = 527 - 454.3103 = \dfrac{ 2108 }{ 29 } \doteq 72.6897= 72.69 \ \text{ EUR } \ \\ \ \\ \ \\ t = a+b = 454.3103+72.6897 = 527 \ \\ q = 100 \cdot \ \dfrac{ b }{ t-b } = 100 \cdot \ \dfrac{ 72.6897 }{ 527-72.6897 } = 16 \ \%$

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