Respuesta :
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
Answer:
There are 68 bicycles, 17 tandem bicycles, and 33 tricycles in the shop.
Step-by-step explanation:
Conventionally, a bicycle has a 1 seat, 1 front handle bars and 2 wheels
A tandem bicycle has 2 seats, 1 front handle bar and 2 wheels
A tricycle has 1 seat, 1 front handle bar and 3 wheels
Let's say;
Number of Bicycles = A
Number of Tandem Bicycles = B
Number of Tricycles = C
We can arrive at the equations for each part of the bikes
Seats → 1A + 2B + 1C = 135 -----1
Front handle bars → 1A + 1B + 1C = 118 -------2
Wheels → 2A + 2B + 3C = 269 ------3
Let's manipulate equation 2 to equation 3 by multiplying equation 2 by 2.
We have 2A + 2B + 2C = 236 -------4
Subtracting Eqt 3 from 4, we have
C = 33
Hence, number of tricycles is 33.
Substituting 33 for C in eqts 1 and 2, we have
1A + 2B = 135 - 33 = 102 -------5
1A + 1B = 118 - 33 = 85 -------6
Multiply eqt 6 by 2, we get
2A + 2B = 170 --------7
Subtract eqt 5 from eqt 7, we have
A = 68
Hence, number of bicycles is 68.
Substitute 68 for A in eqt 6, we have
68 + B = 85
B = 85 - 68 = 17
Hence, number of tandem bicycles is 17.
∴ There are 68 bicycles, 17 tandem bicycles, and 33 tricycles in the shop.
To check,
Eqt 1, 1(68) + 2(17) + 1(33) = 135 (Seats)
Eqt2, 68 + 17 + 33 = 118 (Front handle bars)
Eqt3, 2(68) + 2(17) + 3(33) = 269 (Wheels)
