a total of 135 seats, 118 front handlebars (that steer the bike) and 269 wheels how many bicycles, tandem bicycles, and tricycles are there in the wheel shop

Question

Three months later some vehicles have sold and new models have been brought into the wheel shop. Now, there are different a different numbers of bicycles, tandem bicycles, and tricycles

Answer 1

Lets look at how many of each thing each type of cycle needs.

 

A bicycle has 1 front handlebar, 1 seat, and 2 wheels.

A tandem has 1 front handlebar, 2 seats, and 2 wheels.

A tricycle has 1 front handlebar, 1 seat, and 3 wheels.

 

Let x be the number of bicycles,

let y be the number of tandems,

and let z be the number of tricycles.

 

They all require 1 front handlebar, so with 118 front handlebars, there are a total of 118 cycles.

x+y+z=118

 

The tandem is the only cycle to require more than one seat, so since there are 135-118=17 extra seats, that means there are y=17 tandem bicycles.

 

Finally, we can add up the number of wheels needed:

2x+2y+3z=269

 

We have two equations, with two unknowns (we know y=17):

x+y+z=118

2x+2y+3z=269

 

After substituting in y and simplifying, you can solve for x and z using your favorite method for solving a system of two equations.

 

Please comment if you need more help.