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

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.

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Method 2: Simultaneous equations with two unkowns

Let x be the number of tricycle, and y be the number of bicycle.
x + y = 7 …… [1]
3x + 2y = 19 …… [2]

[1] * 2:
2x + 2y = 14 …… [3]

[2] - [3]:
(3x + 2y) - (2x + 2y) = 19 - 14
n = 5

There were 5 tricycles.

Assuming only numbers of bicycles b and tricycles t present.
2b + 3t = 19
b + t = 7
tricycles t = 5

Six tricycles and a unicycle.

My guess is 7 bicycles and 5 tricycles.  But nobody thought of unicycles or quadricycles.

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

If all 7 were on bicycles it would be 14 wheels, so the 5 extra wheels must be on tricycles.

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 

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

We would need to know the number of unicycles and tandems.

5 tricycles and 2 bicycles

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