Bike Shop question

Question

The Bike Shop sells bicycles and tricycles and often has a selection of them sitting outside for customers to try. Big Bird counted 101 wheels and 42 handlebars of all the bicycles and tricycles. How many bicycles did he see?

Answer 1

Let x = number of bicycles

      y = number of tricycles

 

Each bike and each tricycle have 1 handlebar apiece.  Each  tricycle has 3 wheels and each bicycle has 2 wheels.  

 

So,   x +   y = 42

      2x + 3y = 101

 

Multiply the first equation by -2:    -2x - 2y = -84

                                                              2x + 3y = 101

 

Adding the equations, we get y = 17

                                                    x = 42 - y = 25

 

There are 25 bicycles and 17 tricycles.