A parking lot contains motorcycles (2 wheels) and cars (4 wheels). There are 35 vehicles and 114 wheels. How many motorcycles and cars are
there?
m+c = 35
2m+4c = 114
...
In a full parking lot, there are 35parking spots and 80 wheels. How many cars are there and how many motorcycles are there?
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To find the number of motorcycles and cars in the parking lot, let's assume that x represents the number of motorcycles and y represents the number of cars.
1. Set up equations based on the given information:
- We know that there are a total of 35 vehicles, so the sum of motorcycles and cars should be 35:
x + y = 35
- We also know that the total number of wheels is 114. Since motorcycles have 2 wheels and cars have 4 wheels, we can calculate the total number of wheels using the number of motorcycles (x) and cars (y):
2x + 4y = 114
2. Now we have a system of equations:
x + y = 35
2x + 4y = 114
3. We can use substitution or elimination methods to solve these equations. Let's use the substitution method here:
- Rearrange the first equation: x = 35 - y
- Substitute this expression for x in the second equation:
2(35 - y) + 4y = 114
70 - 2y + 4y = 114
2y = 44
y = 22
4. Now that we know y (the number of cars), we can substitute this value back into the first equation to find x (the number of motorcycles):
x + 22 = 35
x = 35 - 22
x = 13
Therefore, there are 13 motorcycles and 22 cars in the parking lot.