<s>[INST] Is there another simpler method to solve this elementary school math problem? I am teaching an elementary student. He has a homework as follows.

There are $16$ students who use either bicycles or tricycles. The total
  number of wheels is $38$. Find the number of students using bicycles.

I have $3$ solutions as follows.
Using a single variable.
Let $x$ be the number of students in question. The number of students using tricycles is $16-x$. The total number of wheels is the sum of the total number of bicycles times $2$ and the total number of tricycles times $3$.
$$
2\times x + 3 \times (16-x) = 38
$$
The solution is $x=10$.
Using $2$ variables.
Let $x$ and $y$ be the number of students using bicycles and tricycles, respectively.
It implies that
\begin{align}
x+y&=16\\
2x+3y&=38
\end{align}
The solution is $x=10$ and $y=6$.
Using multiples
The multiples of $2$ are $2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22,24, 26,28,30,32,\dotsc$
The multiples of $3$ are $3,6,9,12,15,18,21,24,27,30,33,36,\dotsc$ 
The possible wheel combinations with format $(\#\text{bicycle wheels}, \#\text{tricycle wheels})$:
$\hspace{6cm} (32,6)$ but there are $18$ students
$\hspace{6cm} (26,12)$  but there are $17$ students
$\hspace{6cm} (20,18)$ there are $16$ students
$\hspace{6cm} (14, 24)$ there are $15$ students
$\hspace{6cm} (8, 30)$ there are $14$ students
$\hspace{6cm} (2,36)$ there are $13$ students
Thus the correct combination is $10$ bicycles and $6$ tricycles.
My question
Is there any other simpler method? 
 [/INST] Simplest
Every kid has at least two wheels, $16 \times 2 = 32$ in total. The remaining $38 - 32 = 6$ wheels belong to tricycles, so there are $16 - 6 = 10$ kids on bicycles. 
Trial-and-error
Choose a random integer $x$ between $0$ and $16$ repeatedly until $2x + 3(16 - x)$ equals $38$. If the equality holds, $x$ is the solution. This can be done by hand, using dice or a random number table, but the easiest way is to write a computer program (see the code here).
Root finding
The number of kids on bicycles, $x$, is the root of the first order polynomial $f(x) = 2x + 3(16 - x) - 38 = 10 - x$. The latter form shows directly that the root is $10$. 
It's worth deriving the general formula. Let $m$ and $n$ be the number kids and the number of wheels, respectively. With this notation, $f(x) = 2x + 3(m - x) - n = 3m - n - x$, that is, the root $x = 3m - n$. 
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