There are a different number of bicycles, tandem bicycles, and tricycles in a shop. There a total of 135 seats, 118 front handle bars, and 269 wheels. How many of each bike is there?

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

-6 is the correct option from the above given options

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