Solving equation-systems so it's understandable by an 11 year old

Question

I'm trying to help my little brother with this math homework. The question:

You have three numbers. The sum of these numbers are $7.2$. The second number is twice as large as the first one. The third number is three times as large as the first one.

This is easily solveable by setting up an equation system such as:

$$a + b +c = 7.2$$ $$b = 2a$$ $$c = 3a$$

however, they haven't begun to touch these areas yet. Just trying out numbers and reasoning about it would feel fine if the sum was an integer, now, I have no idea how to help him solve it on his level.

Answer 1

How about this approach:

If the second number is twice as large as the first one, and the third number is three times as large, then all three numbers together are six times as large as the first one alone.

Knowing that all three numbers together also equal $7.2$, an attentive student's intuition should lead him to the solution without any formal arithmetic at all. In particular, it should be immediately apparent what the first number is.

Answer 2

Here’s the first number:

$$\begin{array}{|c|}\hline ?\\ \hline \end{array}$$

Here’s the second number:

$$\begin{array}{|c|c|}\hline ?&?\\ \hline \end{array}$$

And here’s the third number:

$$\begin{array}{|c|c|c|}\hline ?&?&?\\ \hline \end{array}$$

Adding them, we get

$$\begin{array}{|c|c|c|c|c|c|}\hline ?&?&?&?&?&?\\ \hline \end{array}\;,$$

which is plainly the same as

$$\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}\;,$$

just presented more efficiently.

So

$$\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}+\begin{array}{|c|}\hline ?\\ \hline \end{array}=7.2\;,$$

and the first number must be one-sixth of $7.2$.