Pavement around the house

The pavement around the Vyberar family's house has two parts with a total length of 19 metres. The longer part of the pavement is 1 metre shorter than three times the length of the shorter part of the pavement.
Decide for each of the following statements whether it is true, or not.
a) The longer part of the pavement has a length of exactly 14 metres.
b) The lengths of both parts of the pavement are in the ratio 1 : 3.
c) The longer part of the pavement is exactly 9 metres longer than the shorter part.

Result

A=

Yes

No

B=

Yes

No

C = 1

Step-by-step explanation:

$$\begin{gathered} o=19\text{m} \\ a=3b-1 \\ o=a+b \\ 19=a+b \\ a=3\cdot b-1 \\ a-3b=-1 \\ a+b=19 \\ Row2-Row1\to Row2 \\ 4b=20 \\ b=\frac{20}{4}=5 \\ a=-1+3b=-1+3\cdot 5=14 \\ a=14 \\ b=5 \\ a=14m \\ A=1 \end{gathered}$$

$$\begin{gathered} r=b/a=5/14=\frac{5}{14}\doteq 0.3571 \\ B=0 \end{gathered}$$

$$\begin{gathered} \Delta =|a-b|=|14-5|=9\text{m} \\ \Delta =9m \\ C=1 \end{gathered}$$

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