Potatoes bags

I have three bags with 21 kg of potatoes. The first bag has 5.5 kg more potatoes than the second bag, and the third has 0.5 kg more potatoes than the second bag. Determine the weight of each bag.

Correct answer:

a =  10.5 kg
b =  5 kg
c =  5.5 kg

Step-by-step explanation:

$$\begin{gathered} a+b+c=21 \\ a=b+5.5 \\ c=0.5+b \\ a+b+c=21 \\ a-b=5.5 \\ b-c=-0.5 \\ Row2-Row1\to Row2 \\ a+b+c=21 \\ -2b-c=-15.5 \\ b-c=-0.5 \\ Row3-\frac{1}{-2}\cdot Row2\to Row3 \\ a+b+c=21 \\ -2b-c=-15.5 \\ -1.5c=-8.25 \\ c=\frac{-8.25}{-1.5}=5.5 \\ b=\frac{-15.5+c}{-2}=\frac{-15.5+5.5}{-2}=5 \\ a=21-b-c=21-5-5.5=10.5 \\ a=\frac{21}{2}=10.5 \\ b=5 \\ c=\frac{11}{2}=5.5 \end{gathered}$$

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