【Question 28】
In a bicycle shed, there are bicycles (two-wheeled), tricycles, and cars (four-wheeled). It is known that the number of bicycles is four times the number of cars. Several students counted the total number of wheels in the shed, but each one got a different result, which are $235, 236, 237, 238$, and 239. One of these is correct. Smart children, please calculate how many types of quantities of the three kinds of vehicles satisfy the conditions. (For example, if bicycles, tricycles, and cars are $1, 2, 3$ or $3, 2, 1$ respectively, they count as two types.)
【Analysis and Solution】
Indeterminate equation, counting.
Let the number of cars be $x$, the number of bicycles be $4 x$, and the number of tricycles be $y$;
The number of wheels is $4 x \times 2 + y \times 3 + x \times 4 = 12 x + 3 y = 3(4 x + y)$, which is a multiple of 3;
Among them, only 237 is a multiple of 3;
$3(4 x + y) = 237$
$4 x + y = 79$;
$79 \div 4 = 19 \cdots \cdots 3$, so $x$ can take positive integers from $1$ to $19$;
Thus, the positive integer solutions of $4 x + y = 79$ are 19 groups;
Therefore, there are 19 types of the number of the three kinds of vehicles that meet the conditions.