Given:
There are total 15 vehicles and the number of tires is 64.
To find:
The number of motor bikes and cars.
Solution:
a.
Let the number of motor bicycles be x and the number of cars be y.
The total number of vehicles are 15. So,
[tex]x+y=15[/tex]
A motor bike has 2 tires and a car has 4 tires. So,
[tex]\begin{gathered} 2x+4y=64 \\ \Rightarrow x+2y=32 \end{gathered}[/tex]
Thus, the pair of simultaneous equations is:
[tex]\begin{gathered} x+y=15 \\ x+2y=32 \end{gathered}[/tex]
b.
Now, subtract the first equation from the second equation to get,
[tex]\begin{gathered} x+2y-(x+y)=32-15 \\ x+2y-x-y=17 \\ y=17 \end{gathered}[/tex]
If y = 17, then
[tex]\begin{gathered} x+17=15 \\ x=15-17 \\ x=-2 \end{gathered}[/tex]
We get x = -2.
Since the number of motorbikes cannot be negative. Therefore, no solution for this question.
