A tough algebra question that has to do with bikes.?

A shop filled with tandem bikes, regular bikes, and tricycles have a total of 135 seats, 269 wheels, and 118 front handlebars (that steer the bike). How many tandem bikes are there?
Could you also show me how you got the answer? Thanx!

The tandem bokes have two wheels

Let number of tandem = x, regular = y and tricycles = z

Now some tandems have 2 wheels , some have 3, i'm going to base it on them having 2!

2x + y + z = 135
2x + 2y + 3z = 269
x + y + z = 118 (all of these bikes only have one set of FRONT handle bars that STEER the bike!)
solve the system for x
Can do it using matrices (which i like best), but normally you learn the long way first so I will use that...
2x + y + z = 135. ...............(1)
2x + 2y + 3z = 269 ............(2)
x + y + z = 118. ..................(3)
2*(3)
2x + 2y + 2z = 236. ............(4)
(2) - (4)
z = 33
sub this into equation (1)
2x + y + 33 = 135. ...............(1)
2x + y = 102. ...............(5)
and equation (3)
x + y + 33 = 118. ..................(3)
x + y = 85. ..................(6)
(5) - (6)
x = 102-85
= 17

there are 17 tandem bikes

Tandem bikes have 2 seats, 2 wheels, and 1 front handlebar
Regular bikes have 1 seat, 2 wheels, and 1 front handlebar
Tricycles have 1 seat, 3 wheels, and 1 front handlebar

Let T, R, and Y be the number of Tandems, Regulars, and Trikes, respectively. Then we have the equations:

2T + R + Y = 135
2T + 2R + 3Y = 269
T + R + Y = 118

Subtract line 3 from line 1, and you get T = 17
Double line 3, subtract that from line 2, and you get Y = 33
Plug those numbers into line 3, and R = 68

Hopefully

it doesn't matter how many wheels the tandems have


there are 17 more seats than handel bars
each unit has 1 handel bar, the tandems have 2 seats
each extra seat is a tandem

17 tandems
no algebra just logic

wow scrander drinks too much coffee!

Ignore the wheels. Everything has 1 handlebar, so there are 118 cycles total. They all have at least one seat, so 135 seats minus 118 cycles leaves 17 spare saddles. Only tandems have two saddles, so there must be 17 tandems.