Gunpowder component mixture

Gunpowder is made from a mixture of coal, sulfur, and lignite, with 4 times more lignite than sulfur and 3 times more sulfur than coal. Calculate how many kilograms of individual components are needed to produce 240 kg of gunpowder.?

Final Answer:

u =  15 kg
s =  45 kg
l =  180 kg

Step-by-step explanation:

$$\begin{gathered} m=240\text{kg} \\ l=4s \\ s=3u \\ l=12u \\ u=3u \\ {r}_1=\frac{1}{12+3+1}=\frac{1}{16}=0.0625 \\ {r}_2=\frac{12}{12+3+1}=\frac{3}{4}=0.75 \\ {r}_3=\frac{3}{12+3+1}=\frac{3}{16}=0.1875 \\ u=r_1\cdot m=0.0625\cdot 240=15\text{kg} \end{gathered}$$

$s=r_3\cdot m=0.1875\cdot 240=45\text{kg}$

$l=r_2\cdot m=0.75\cdot 240=180\text{kg}$

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