The number that satisfies the equation a + a = a a a is 3. This can be demonstrated through algebraic manipulation. Let's denote the unknown number as x. The equation becomes:

a + a = a a a

Simplifying the left side, we have:

2a = a a a

Now, let's consider the right side. The notation "a a a" can be interpreted as a repeated multiplication of a by itself, which is equivalent to a^3. Therefore, the equation becomes:

2a = a^3

To solve for a, we can rearrange the equation to:

a^3

2a = 0

Factoring out an a, we get:

a(a^2

2) = 0

This equation has two solutions: a = 0 and a^2

2 = 0. The second solution leads to:

a^2 = 2

Taking the square root of both sides, we find:

a = √2

However, since we are looking for a whole number solution, we discard √2 and consider the first solution, a = 0. Plugging this back into the original equation, we see that it holds true:

0 + 0 = 0 0 0

Thus, the number that satisfies the equation a + a = a a a is 0.

The reason this equation has a whole number solution is due to the properties of multiplication and addition. When a is a whole number, the equation simplifies to 2a = a^3, which can be factored to a(a^2 - 2) = 0. The only whole number solution to this equation is a = 0. This result is consistent with the properties of whole numbers and their operations, as well as the fundamental principles of algebra.