# Bonus

Gross wage was 527 EUR including 16% bonus.

How many EUR were bonuses?

Correct result:

b =  72.69 EUR

#### Solution:

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

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