In a shop selling bicycle and tricycle, a total of 80 pedals and a total of 98 wheels were counted. How many bicycles and tricycles does he have?
number of bikes --- b
number of trikes--- t
(assume: a bike has 2 pedals and 2 wheels, a trike has 2 pedals and three wheels)
2b+2t = 80 --- > b = 40-t
2b + 3t = 98
2(40-t) + 3t = 98
80-2t+3t=98
t=18
b = 22
He has 22 bikes and 18 trikes
To solve this problem, let's use a system of equations.
Let's assume the number of bicycles is represented by 'x' and the number of tricycles is represented by 'y'.
Each bicycle has 2 wheels and each tricycle has 3 wheels, so we can create the first equation:
2x + 3y = total number of wheels (98)
Similarly, each bicycle has 2 pedals and each tricycle has 3 pedals, so we can create the second equation:
2x + 3y = total number of pedals (80)
Now, we have a system of equations:
2x + 3y = 98
2x + 3y = 80
We can solve this system of equations to find the values of x and y.
Subtracting the second equation from the first equation:
(2x + 3y) - (2x + 3y) = 98 - 80
0 = 18
This equation is inconsistent with no solution. It means that there is no valid combination of bicycles and tricycles that would satisfy the given conditions. There might be a mistake in the given information or calculation.
Therefore, based on the information provided, we cannot determine the number of bicycles and tricycles in the shop.