A parking lot contains a total of 52 cars and motorcycles. There are a total of 186 tires (not counting spare tires) in the lot. Assuming each car has 4 tires and each motorcycle has 2 tires, determine how many cars and how many motorcycles are in the parking lot.
Let's assume the number of cars in the parking lot is C, and the number of motorcycles is M.
According to the information given:
1. The total number of vehicles is 52: C + M = 52.
2. The total number of tires is 186: 4C + 2M = 186.
We can solve these two equations simultaneously to find the values of C and M.
Step 1: Solve the first equation for C in terms of M:
C = 52 - M.
Step 2: Substitute this value of C into the second equation:
4(52 - M) + 2M = 186.
Step 3: Simplify and solve for M:
208 - 4M + 2M = 186.
-2M = 186 - 208.
-2M = -22.
M = (-22)/(-2).
M = 11.
Step 4: Substitute the value of M back into the first equation to find C:
C + 11 = 52.
C = 52 - 11.
C = 41.
Therefore, there are 41 cars and 11 motorcycles in the parking lot.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the number of cars in the parking lot is represented by 'C', and the number of motorcycles is represented by 'M'.
From the given information, we know that there are a total of 52 cars and motorcycles combined. So, we can write the equation: C + M = 52.
We also know that the total number of tires in the lot (not counting spare tires) is 186. Since each car has 4 tires and each motorcycle has 2 tires, we can write the equation: 4C + 2M = 186.
Now we have a system of equations:
C + M = 52 (Equation 1)
4C + 2M = 186 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of substitution. We can rearrange Equation 1 to express C in terms of M: C = 52 - M.
Now substitute this value of C in Equation 2:
4(52 - M) + 2M = 186.
Simplify the equation:
208 - 4M + 2M = 186
208 - 2M = 186
-2M = 186 - 208
-2M = -22
M = -22 / -2
M = 11.
So, there are 11 motorcycles in the parking lot.
Substitute this value of M into Equation 1 to find the number of cars:
C + 11 = 52
C = 52 - 11
C = 41.
Therefore, there are 41 cars in the parking lot.
To summarize, there are 41 cars and 11 motorcycles in the parking lot.
cars ---- x
bikes ----y
x+y = 52
4x + 2y = 186 or
2x + y = 93
subract:
x = 41
then 41 + y = 52 ---> y = 11
There are 41 cars and 11 bikes.