there are 65 tricycles and bicycles in a parking lot. if there are 153 wheels, how many tricycles are there?
t + b = 65
3 t + 2 b = 153
solve the system
To find the number of tricycles in the parking lot, we need to set up an equation using the given information.
Let's assume x represents the number of tricycles and y represents the number of bicycles.
We know that the total number of tricycles and bicycles is 65, so we can write the equation:
x + y = 65 ----(equation 1)
We also know that there are 153 wheels in total. A tricycle has 3 wheels, while a bicycle has 2 wheels. So, we can write another equation considering the wheels:
3x + 2y = 153 ----(equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve using the method of elimination:
Multiplying equation 1 by 3, we get:
3x + 3y = 195 ----(equation 3)
Now, subtract equation 2 from equation 3:
(3x + 3y) - (3x + 2y) = 195 - 153
3x + 3y - 3x - 2y = 42
y = 42
Now, substitute the value of y into equation 1:
x + 42 = 65
x = 65 - 42
x = 23
Therefore, there are 23 tricycles in the parking lot.