# Alice counted 7 cycle riders and 19 cycle wheel going past her house. How many tricycle were there?

Relevance
• By common sense, there are 2 kinds of cycles on the road; one is the bicycle the other one is tricycle. So, let

b=the number of bicycles

t=the number of tricycles

b+t=7

2b+3t=19

=>

2(7-t)+3t=19

=>

14-2t+3t=19

=>

t=5.

• In doing this  kind of homework problem, state your assumptions.

- There are only bicycle and tricycle riders.  No uniccles, adult 4-wheel pedal carts.

- There is one, and exactly one, rider per cycle.  No tandem bikes, no riderless self-riding bicycle.

Then if b is the number of bicycles, and t the number of tricycles,

b + t = 7  ; total number of riders

2b + 3t = 19  ; bike has 2 wheels, trike has 3

You now have 2 equations in 2 unknowns.  If you need help in proceeding, I'm sure another answer will spell it out for you.

• Alice counted 7 cycle riders and 19 cycle wheels going past her house.

How many tricycles were there?

b + t = 7

2b + 3t = 19

t = 5

• 6   as 3X6 is 18  The seventh rider was on a Unicycle.

• 2*2+5*3=4+15=                      .19

• if bicycles, and tricycles:     2..... bicycles = 4 wheels.....5 tricycles= 15  wheels...…,  4 wheels plus 15 wheels= 19 wheels......answer is 5

• 5 tricycles and 2 bicycles

• Assuming only numbers of bicycles b and tricycles t present.

2b + 3t = 19

b + t = 7

tricycles t = 5

• Method 1: Linear equation with one unknown

Let n be the number of tricycles.

Then, the number of bicycles = (7 - n)

Total number of wheels:

3n + 2(7 - n) = 19

3n - 14 - 2n = 19

n = 5

There were 5 tricycles.

====

Method 2: Simultaneous equations with two unkowns

Let x be the number of tricycle, and y be the number of bicycle.

x + y = 7 …… 

3x + 2y = 19 …… 

 * 2:

2x + 2y = 14 …… 

 - :

(3x + 2y) - (2x + 2y) = 19 - 14

n = 5

There were 5 tricycles.

• Six tricycles and a unicycle.