Kilometers 29551

The Poznáváky family traveled by car for 3 days in Slovakia. On the first day, they covered twice as many kilometers as on the second day, and on the third day, they covered 50 kilometers more than on the second day. They drove a total of 700 kilometers in all 3 days. How many kilometers did they drive on the first day?

Correct answer:

a =  130 km

Step-by-step explanation:

$$\begin{gathered} a+b+c=700 \\ a=b/2 \\ c=50+b \\ a+b+c=700 \\ 2a-b=0 \\ b-c=-50 \\ Pivot:Row1\leftrightarrow Row2 \\ 2a-b=0 \\ a+b+c=700 \\ b-c=-50 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a-b=0 \\ 1.5b+c=700 \\ b-c=-50 \\ Row3-\frac{1}{1.5}\cdot Row2\to Row3 \\ 2a-b=0 \\ 1.5b+c=700 \\ -1.667c=-516.667 \\ c=\frac{-516.66666667}{-1.66666667}=310 \\ b=\frac{700-c}{1.5}=\frac{700-310}{1.5}=260 \\ a=\frac{0+b}{2}=\frac{0+260}{2}=130 \\ a=130 \\ b=260 \\ c=310 \end{gathered}$$

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