Cork and swimming

If a person weighs 80 kg, how many kilograms of cork must take a swimming belt to float on water? The density of the human body is 1050 kg/m³, and the cork is 300 kg/m³.

(Instructions: Let the human body and cork on a mixture with a density of 1000kg/m³. When you make the equation, you will compare the volumes of both components and the resulting mixture volume.)

Correct answer:

x =  1.6327 kg

Step-by-step explanation:

$$\begin{gathered} a=80\text{kh} \\ {h}_1=1050{\text{kg/m}}^3 \\ {h}_2=300{\text{kg/m}}^3 \\ {h}_3=1000{\text{kg/m}}^3 \\ h=m/V \\ V=m/h \\ a/h_1+x/h_2=(a+x)/h_3 \\ 80/1050+x/300=(80+x)/1000 \\ 49x=80 \\ x=\frac{80}{49}=1.63265306 \\ x=\frac{80}{49}\doteq 1.632653=1.6327\text{kg} \end{gathered}$$

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