How many bicycles, tandem bicycles and tricycles are there in the wheel shop?

Question

If there are a total of 135 seats, 118 front handlebars (that steer the bike), and 269 wheels.

Answer 1

X is # of bicycles

Y is # of tandem bicycles

Z is # of tricycles

 

X+2Y + Z = 135 <--- seats

 

X+Y+Z = 118 <--- handlebars

 

2X + 2Y + 3Z = 269 <--- wheels

 

Subtracting the second equation from the first: Y = 17

Plugging this in the system becomes:

 

X+Z = 101

2X + 3z = 235

 

The top equation , solved for Z is 101-X, so Z=101 - x

Substituting into the bottom equation:

 

2x + 3(101 - x) = 235

2x + 303 - 3x = 235

 

-x = 235 - 303

 

-x = -68

 

x = 68

 

Using the original second equation:

x+y+z = 118

 

68 + 17 + z = 118

 

85 + z = 118

 

z = 118 - 85 = 33

 

CHECK:

68 + 2(17) + 33 = 68 + 34 + 33 = 68 + 67 = 135

 

68+ 17 + 33 = 68 + 50 = 118

 

2x + 2y + 3z = 2(68) + 2(17) + 3(33) = 136 + 34 + 99= 136 + 133 = 269

 

68 bicycles

17 tandem bicycles

33 tricycles

 

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