Alloy Cu+Pb

An alloy of copper and lead is a mixture of these metals in a ratio of 5:2 (respectively).
Calculate in kg how much a piece of this alloy weighs if it contains just 150 kg less lead than copper.

Correct answer:

m =  350 kg

Step-by-step explanation:

$$\begin{gathered} a=5/2\cdot b \\ a=b+150 \\ 2a-5b=0 \\ a-b=150 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a-5b=0 \\ 1.5b=150 \\ b=\frac{150}{1.5}=100 \\ a=\frac{0+5b}{2}=\frac{0+5\cdot 100}{2}=250 \\ a=250 \\ b=100 \\ m=a+b=250+100=350\text{kg} \end{gathered}$$

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