Car showroom 2

A car showroom sells cars - several brands. Over the past month, 61 vehicles in total were sold. Cars equipped with air conditioning were sold three times more than cars of the Škoda brand. Škoda cars which were not equipped with air conditioning were sold 6 fewer than Škodas with air conditioning. Cars which were not of the Škoda brand and did not have air conditioning were sold 3 more than Škoda cars without air conditioning. How many Škodas were sold? How many air-conditioned vehicles of another brand than Škoda were sold?

Final Answer:

x =  16
d =  37

Step-by-step explanation:

$$\begin{gathered} a+b+c+d=61 \\ c+d=3\cdot (a+c) \\ a=c-6 \\ b=3+a \\ a+b+c+d=61 \\ 3a+2c-d=0 \\ a-c=-6 \\ a-b=-3 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ b+0.3333c+1.3333d=61 \\ Row3-\frac{1}{3}\cdot Row1\to Row3 \\ -1.6667c+0.3333d=-6 \\ Row4-\frac{1}{3}\cdot Row1\to Row4 \\ -b-0.6667c+0.3333d=-3 \\ Row4+Row2\to Row4 \\ -0.3333c+1.6667d=58 \\ Row4-\frac{-0.33333333}{-1.66666667}\cdot Row3\to Row4 \\ 1.6d=59.2 \\ d=\frac{59.2}{1.6}=37 \\ c=\frac{-6-0.33333333333333d}{-1.66666667}=\frac{-6-0.33333333\cdot 37}{-1.66666667}=11 \\ b=61-0.33333333333333c-1.3333333333333d=61-0.33333333\cdot 11-1.33333333\cdot 37=8 \\ a=\frac{0-2c+d}{3}=\frac{0-2\cdot 11+37}{3}=5 \\ a=5 \\ b=8 \\ c=11 \\ d=37 \\ x=a+c=5+11=16 \end{gathered}$$

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