Semi-skimmed 82206

The dairy produces semi-skimmed milk (with 1.5% fat content) by skimming part of the fat from full-fat milk (with 4% fat content). 1 ton of semi-skimmed milk is produced from how many kilograms of fat milk?

Correct answer:

m₁ =  1026.04 kg

Step-by-step explanation:

$$\begin{gathered} m_2=1\text{t}\to \text{kg}=1\cdot 1000\text{kg}=1000\text{kg} \\ {r}_2=1.5\%=\frac{1.5}{100}=0.015 \\ {r}_1=4\%=\frac{4}{100}=\frac{1}{25}=0.04 \\ {w}_1=1-r_1=1-0.04=\frac{24}{25}=0.96 \\ {w}_2=1-r_2=1-0.015=\frac{197}{200}=0.985 \\ {H}_{2}O: \\ {w}_1\cdot m_1=w_2\cdot m_2 \\ {m}_1=\frac{w_2}{w_1}\cdot m_2=\frac{0.985}{0.96}\cdot 1000=1026.04\text{kg} \end{gathered}$$

Try another example