Sea water

Mixing 62 kg of sea water with 84 kg rainwater is created water containing 3.1% salt. How many percent sea water contains salt?

Result

x =  7.3 %

Solution:

$m_{1}=62 \ \text{kg} \ \\ m_{2}=84 \ \text{kg} \ \\ \ \\ p=3.1 \ \% \ \\ \ \\ p=100 \cdot \ \dfrac{ \dfrac{ x }{ 100 } \cdot \ m_{1} }{ m_{1}+m_{2} } \ \\ \ \\ p \cdot \ \dfrac{ m_{1}+m_{2} }{ 100 }=\dfrac{ x }{ 100 } \cdot \ m_{1} \ \\ \ \\ p \cdot \ (m_{1}+m_{2})=x \cdot \ m_{1} \ \\ \ \\ x=p \cdot \ \dfrac{ m_{1}+m_{2} }{ m_{1} }=3.1 \cdot \ \dfrac{ 62+84 }{ 62 }=\dfrac{ 73 }{ 10 }=7.3=7.3 \%$

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