a number added to its two-thirds is equal to 55. find the number.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Write the equation based on the problem statement
According to the problem, the number added to its two-thirds is equal to 55. This can be expressed mathematically as:
\[ x + \frac{2}{3}x = 55 \]

### Step 3: Combine like terms
To combine the terms on the left side, we need to express \( x \) as a fraction:
\[ x = \frac{3}{3}x \]
Now we can rewrite the equation:
\[ \frac{3}{3}x + \frac{2}{3}x = 55 \]
This simplifies to:
\[ \frac{3x + 2x}{3} = 55 \]
Which further simplifies to:
\[ \frac{5x}{3} = 55 \]

### Step 4: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 3:
\[ 5x = 55 \times 3 \]
Calculating the right side gives:
\[ 5x = 165 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 5 to find \( x \):
\[ x = \frac{165}{5} \]
Calculating this gives:
\[ x = 33 \]

### Step 6: Conclusion
The number we are looking for is \( 33 \).