There are total of 40 cars and motorcycles in a car park. Altogether, 108 wheels are counted. How many cars and how many motorcycles are there in the car park?
c+m = 40 **
4c + 2m = 108 or
2c + m = 54 ***
subtract ** from ***
c = 14 , then m = 26
we have 14 cars and 26 motorbikes
To solve this problem, let's assign variables to represent the number of cars and motorcycles.
Let's say:
C = number of cars
M = number of motorcycles
Since we know that there are a total of 40 vehicles and 108 wheels, we can set up a system of equations based on the number of wheels each type of vehicle has:
Cars have 4 wheels each, so the total number of wheels contributed by the cars is 4C.
Motorcycles have 2 wheels each, so the total number of wheels contributed by the motorcycles is 2M.
From the problem statement, we also know that the total number of wheels is 108:
4C + 2M = 108 -- Equation 1
Additionally, we know that the total number of vehicles is 40:
C + M = 40 -- Equation 2
Now we have a system of equations. We can solve it by substituting the value of C from Equation 2 into Equation 1:
4(40 - M) + 2M = 108
160 - 4M + 2M = 108
-2M = 108 - 160
-2M = -52
M = -52 / -2
M = 26
Substituting the value of M back into Equation 2:
C + 26 = 40
C = 40 - 26
C = 14
Therefore, there are 14 cars and 26 motorcycles in the car park.