Please help me on this math problem... how many tandem bikes??

A shop filled with bicycles, tricyles, and tandem bicycles has a total of 135 seats, 269 wheels, and 118 front handles for steering. How many tandem bikes are there>?

17 tandems (the difference between front handles and seats)

treat bikes and tandems as a single unit B
they each have one front handle and two wheels
trikes have one front handle and 3 wheels (T)
3T + 2B = 269
T + B = 118 --> 2T + 2B = 236

subtracting, T = 33 (so 99 wheels, 33 front handles /33 seats)
B = 85 (so 170 wheels, 85 front handles)

of the 85 Bikes, you need 135 - 33 = 102 seats
102 = 85 + 17, so you have 17 tandems and 68 regular bikes

totals:
17 tandems (17 front handles, 34 seats, 34 wheels)
68 bikes (68 front handles, 68 seats, 136 wheels)
33 trikes (33 front handles, 33 seats, 99 wheels)

altogether: 118 front handles, 135 seats, 269 wheels

17

There are 135 seats and 118 front handles. All the bicycles, tandem bicycles, and tricycles have 1 handle. All have 1 seat except for the tandem bike, which has two.

So the only reason the number of seats can be different from the number of handles is the tandem bikes. For each tandem bike, the total number of seats will be one greater than the number of front handles.

STALKER REPORT 223418: You are an 8th grader attending Thornton Junior High School in Fremont, CA, USA zip code 94526