Algebra Problem: Find the Value of A in A + AA + AAA = 738

Solve the algebraic equation A + AA + AAA = 738 to find the value of the digit A. The solution involves simplifying the equation and solving for A.

Answer

The problem is to find the value of the digit A such that the equation

is true.

The notation

represents a two-digit number where both digits are A. This can be written as

.
The notation

represents a three-digit number where all digits are A. This can be written as

So the equation can be rewritten as:

Combine the terms on the left side of the equation:

To find the value of A, divide both sides of the equation by 123:

Now, we need to perform the division. We can estimate the value of A. Since

and

, it seems that A is 6.
Let’s verify the multiplication:

So,

Now let’s check if this value of A satisfies the original equation:

The equation is satisfied.

The final answer is

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Algebra Problem: Find the Value of A in A + AA + AAA = 738

Question

Answer

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