Solve the following problem using a method of your choice. A store clerk who is taking inventory in a toy store of bicycles and tricycles in a certain way. He commented that there are 50 wheels and 40 pedals. How many bicycles and how many tricycles did he have?
This is probably an exercise on system of equations. However, this can be solved mentally.
40 pedals => 20 pedaling vehicles.
If all bicycles, there are 40 wheels, so we are 10 wheels short. Change 10 bicycles for 10 tricycles will solve that.
So there are 10 bicycles and 10 tricycles.
Check: 20 wheels for 10 bicyles and 30 wheels for 10 tricycles make 50 wheels.
To solve this problem, we can use a system of equations. Let's represent the number of bicycles as 'b' and the number of tricycles as 't'.
Each bicycle has two wheels and two pedals, while each tricycle has three wheels and two pedals. We can write the following equations based on the given information:
2b + 3t = 50 (equation 1)
2b + 2t = 40 (equation 2)
To solve this system of equations, we can use a variety of methods, such as substitution, elimination, or graphing. Here, I will use the method of elimination by multiplying equation 2 by -1, then adding it to equation 1.
(-1)(2b + 2t) = (-1)(40)
-2b - 2t = -40
2b + 3t - 2b - 2t = 50 - 40
t = 10
Now, substitute the value of t back into equation 2 to find the number of bicycles:
2b + 2(10) = 40
2b + 20 = 40
2b = 20
b = 10
The store clerk has 10 bicycles and 10 tricycles.