Distances 64024

Eleven trees are planted on the street at equal distances. If they planted three more trees, the spaces between them would be 12 m shorter. What is the distance in meters between the first and the last tree?

Correct answer:

x =  520 m

Step-by-step explanation:

$$\begin{gathered} x=(11-1)\cdot a \\ x=(14-1)\cdot (a-12) \\ 10a-x=0 \\ 13a-x=156 \\ Pivot:Row1\leftrightarrow Row2 \\ 13a-x=156 \\ 10a-x=0 \\ Row2-\frac{10}{13}\cdot Row1\to Row2 \\ 13a-x=156 \\ -0.23x=-120 \\ x=\frac{-120}{-0.23076923}=520 \\ a=\frac{156+x}{13}=\frac{156+520}{13}=52 \\ a=52 \\ x=520=520\text{m} \end{gathered}$$

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