In a parking lot there are motorcycles and cars. There are 48 motors and 136 tires. How many motorcycles and how many cars are in the parking lot?
let x = #motorcycles
and y = # cars
-----------------
x+y = 48 motors
2x + 4y = 136 tires
Solve the two equations simultaneously for x and y
To solve this problem, we can set up a system of equations. Let's denote the number of motorcycles as "m" and the number of cars as "c".
Since there are 48 motors in total, we can write the equation:
m + c = 48 ----(1)
Now, let's consider the number of tires. Each motorcycle has 2 tires, and each car has 4 tires. The total number of tires can be expressed as:
2m + 4c = 136 ----(2)
We now have a system of two equations with two variables. We can solve this system to find the values of "m" and "c".
First, let's rewrite equation (1) to solve for "m":
m = 48 - c
Substituting this value of "m" into equation (2), we get:
2(48 - c) + 4c = 136
96 - 2c + 4c = 136
2c = 136 - 96
2c = 40
c = 20
Now that we know the value of "c" is 20, we can substitute it back into equation (1) to find the value of "m":
m + 20 = 48
m = 48 - 20
m = 28
Therefore, there are 28 motorcycles and 20 cars in the parking lot.