Find the number of bicycles and tricycles Help for my son.  My math is a bit rusty and I'm trying to remember how to go about answering this question:  "There are 3 times as many bicycles in the playground as there are tricycles.  There is a total of 81 wheels.  What is the total number of bicycles and tricycles in the playground?"     
 A: Denote the number of bicycles by $b$ and the number of tricycles by $t$. 
You know that $b = 3t$ from "3 times as many bicycles in the playground as there are tricycles." and you know that $2b + 3t = 81$ as the total number of wheels is the number of bicycles times $2$ (two wheels per bike) plus the number of tricycles times $3$ (three wheels per bike). 
Now you can plug in $3t$ for $b$ in the second equation to get $2 (3t) + 3t = 81$ so $9t = 81$. From there you get $t$ and then $b$ by the first equation. 
It is possible that your son is not really supposed to use more than one variable. 
In this case call the number of tricycles $t$ and argue that $2(3t) + 3t =81$ in about the same was as above.
A: Just solve the following system of equations
$$\begin{array}{lll}
b-3t&=&0\\
2b+3t&=&81\\
\end{array}$$
A: One way to wring the equations out of the word problem is to start with made-up numbers, and then abstract the letters.
"There are three times as many bicycles as tricycles."  So if we have $4$ tricycles, then we have three times as many bicycles, which is $12$.  Abstracting, if we have $T$ tricycles, then we have $B=3T$ bicycles.
Same with the wheels.  If we have $12$ bikes, then we have twice as many wheels, which is $24$ wheels.  So the number of bike wheels is $W_B = 2B$.
Likewise, the number of trike wheels is $W_T = 3T$.
The last piece of information we know is that the total number of wheels is $81$:  $W_B + W_T = 81$.
Now, we substitute to solve for either the number of bikes $B$ or the number of trikes $T$:
$$W_B + W_T = 2B + 3T = 2(3T) + 3T = 9T = 81,$$
so the number of trikes is $T=9$.  Then, the number of bikes is
$$B = 3T = 3(9) = 27.$$
And we can have some assurance we're right by calculating the number of wheels:
$$W_B + W_T = 2B + 3T = 2(27) + 3(9) = 54 + 27 = 81.$$
A: B = 3T. (B for Bycicle, T for Trycicle).
2B + 3T = 81 (wheels)
Just replace B for 3T:  2(3T) + 3T = 81.
That gives you: 9T = 81. So there are 9 tricycles.
Therefore B = 3*9 = 27 (bicycles)
A: 1: 3t = b (three times as many bikes as trikes)
2: 2b + 3t = 81 (each bike has two wheels, trike three wheels, totaling 81)
Solving:
3: b - 3t = 0 (from line 1, moving 3t to the other side)
4: 2b - 6t = 0 (multiplying both sides by 2)
5: 9t = 81 (subtracting line 4 from line 2)
6: t = 9 (dividing both sides by 9)
7: b = 27 (substituting 9 into line 1)
A: \begin{align}
&\text{Number of bicycles} =3 \times 2x\text{ wheels}\\
&\text{Number of tricycles} =3x\text{ wheels}\\
&3 \times 2x\text{ wheels}\ +\ 3x\text{ wheels}=81\text{ wheels}\\
&9x=81\\
&x=9\\
&\text{Number of bicycles} =3 \times 9\\
&\text{Number of tricycles} =9\\
\end{align}
A: Without using equations and variables:

There are 3 times as many bicycles in the playground as there are
  tricycles.

Make groups of three bicycles and one tricycle each. Each group consists of 4 toys and has 9 wheels.

There is a total of 81 wheels. 

There are 9 groups and thus 36 toys on the playground.
A: Hint:  Let there be $b$ bikes and $t$ trikes.  Each sentence provides an equation, giving two simultaneous equations in two unknowns.  Or group three bikes with a trike (based on the first sentence).  How many wheels does it have?  How many groups are there?
A: There are N tricycles and each tricycle has 3 wheels
There are (3 * N) bicycles and each bicycle has 2 wheels
Number of Wheels = 81
(Number of tricycles * Number of Wheels per tricycle) + (Number of bicycle * Number of wheels per bicycle) = Total Wheels
(N * 3) + (3N * 2) = 81
3N + 6N = 81
9N=81
N= 81/9 = 9
So total number of bicycles in the playground = 3*N = 29
total number of tricycles in the playground = N = 9
