# Election mathematics

In elections, 12 political parties received this shares of voters:

party A 56.2 %
party B 8.5 %
party C 8.2 %
party D 6.2 %
party E 6.1 %
party F 5.5 %
party G 3.2 %
party H 2.1 %
party I 2 %
party J 1 %
party K 1 %

Calculate what the shares acquired in the parliament, if a quorum is 5%.

Result

A =  62 %
B =  9.4 %
C =  9 %
D =  6.8 %
E =  6.7 %
F =  6.1 %
G =  0 %
H =  0 %
I =  0 %
J =  0 %
K =  0 %

#### Solution:

$A=56.2 \cdot \ (100/(0+56.2+8.5+8.2+6.2+6.1+5.5+0+0+0+0+0)) \doteq 61.9625=62 \%$
$B=8.5 \cdot \ (100/(0+56.2+8.5+8.2+6.2+6.1+5.5+0+0+0+0+0))=\dfrac{ 8500 }{ 907 } \doteq 9.3716 \doteq 9.4 \%$
$C=8.2 \cdot \ (100/(0+56.2+8.5+8.2+6.2+6.1+5.5+0+0+0+0+0))=\dfrac{ 8200 }{ 907 } \doteq 9.0408 \doteq 9 \%$
$D=6.2 \cdot \ (100/(0+56.2+8.5+8.2+6.2+6.1+5.5+0+0+0+0+0))=\dfrac{ 6200 }{ 907 } \doteq 6.8357 \doteq 6.8 \%$
$E=6.1 \cdot \ (100/(0+56.2+8.5+8.2+6.2+6.1+5.5+0+0+0+0+0))=\dfrac{ 6100 }{ 907 } \doteq 6.7255 \doteq 6.7 \%$
$F=5.5 \cdot \ (100/(0+56.2+8.5+8.2+6.2+6.1+5.5+0+0+0+0+0))=\dfrac{ 5500 }{ 907 } \doteq 6.0639 \doteq 6.1 \%$
$G=0=0 \%$
$H=0=0 \%$
$I=0=0 \%$
$J=0=0 \%$
$K=0=0 \%$

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