Carrots and potatoes

Juri is doing his weekly grocery shop and buying carrots and potatoes. He calculates that the average weight of a carrot is 60 g and the average weight of a potato is 125 g. Furthermore, he calculates that the average weight of the carrots and potatoes he purchases is 86 g. If Yuri's shopping weighed 1.29 kg, how many of each did he purchase?

Correct answer:

a =  9
b =  6

Step-by-step explanation:

$$\begin{gathered} m=1.29\text{kg}\to \text{g}=1.29\cdot 1000\text{g}=1290\text{g} \\ 60a+125b=m \\ 86\cdot (a+b)=m \\ 60a+125b=1290 \\ 86\cdot (a+b)=1290 \\ 60\cdot a+125\cdot b=1290 \\ 86\cdot (a+b)=1290 \\ 60a+125b=1290 \\ 86a+86b=1290 \\ Pivot:Row1\leftrightarrow Row2 \\ 86a+86b=1290 \\ 60a+125b=1290 \\ Row2-\frac{60}{86}\cdot Row1\to Row2 \\ 86a+86b=1290 \\ 65b=390 \\ b=\frac{390}{65}=6 \\ a=\frac{1290-86b}{86}=\frac{1290-86\cdot 6}{86}=9 \\ a=9 \\ b=6 \end{gathered}$$

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