Answer: there are 68 bicycles, 17 tandem bicycles and 33 tricycles.
Step-by-step explanation:
Let x represent the number of bicycles there.
Let y represent the number of tandem bicycles there.
Let z represent the number of tricycles there.
The bicycle and the tricycle has 1 seat each while the tandem bicycle has 2 seats. There a total of 135 seats. This means that
x + 2y + z = 135- - - - - - - - - - - - - - 1
Each of them has 1 front handle bars. The total number of front handle bars is 118. This means that
x + y + z = 118 - - - - - - - - - - - - -2
The bicycle and the tandem bicycle has 2 wheels each while the tricycle has 3 wheels. The total number of wheels is 118. This means that
2x + 2y + 3z = 269 - - - - - - - - - - -3
Subtracting equation 2 from equation 1, it becomes
2y - y = 135 - 118
y = 17
Substituting y = 17 into equation 1 and equation 3, it becomes
x + 17 + z = 118
x + z = 118 - 17
x + z = 101
x = 101 - z
2x + 2 × 17 + 3z = 269
2x + 34 + 3z = 269
2x + 3z = 269 - 34
2x + 3z = 235 - - - - - - - - - - - -3
Substituting x = 101 - z into equation 3, it becomes
2(101 - z) + 3z = 235
202 - 2z + 3z = 235
- 2z + 3z = 235 - 202
z = 33
x = 101 - z = 101 - 33
x = 68
