How many bikes and trikes are there?

Question

There are some bikes and trikes on the playground. There are 7 seats and 19 wheels. How many bikes are there? How many trikes are there?

Answer 1

Let b = the number of bikes and t = the number of trikes.  Each trike and bike has only one seat.  A bike has two wheels while a trike has 3 wheels.

 

Since there are 7 seats, we know that:

 

b + t = 7, so t = 7 - b

 

There are 19 wheels:

 

19 = 2*b + 3*t

 

Substitute 7-b in place of t:

 

19 = 2b + 3 (7-b)

19 = 2b + 21 - 3b

19 = 21 - b

-2 = -b

 

2 = b

 

t = 7-b = 7-2 = 5

 

There are 2 bikes and 5 trikes on the playground.

 

Check:

19 = 2*b + 3*t

19 = 2+2 + 3*5

19 = 2 + 15

19 = 19

Check!!!