In a two-digit number the digit in the unit's place is three times the digit in the tenth's place. The sum of the digits is equal to 8. Then, what is the number?

Options

A. 20
B. 26
C. 39
D. 13

Answer

To solve the problem, we will denote the digits of the two-digit number as follows:

Let:
- \( x \) = digit in the ten's place
- \( y \) = digit in the unit's place

From the problem, we have two key pieces of information:

1. The digit in the unit's place is three times the digit in the ten's place:
\[ y = 3x \]

2. The sum of the digits is equal to 8:
\[ x + y = 8 \]

Now, we can substitute the first equation into the second equation.

### Step 1: Substitute \( y \) in the sum equation
Substituting \( y = 3x \) into the equation \( x + y = 8 \):
\[ x + 3x = 8 \]

### Step 2: Combine like terms
Combine the terms on the left side:
\[ 4x = 8 \]

### Step 3: Solve for \( x \)
Now, divide both sides by 4 to solve for \( x \):
\[ x = \frac{8}{4} = 2 \]

### Step 4: Find \( y \)
Now that we have \( x \), we can find \( y \) using the first equation:
\[ y = 3x = 3 \times 2 = 6 \]

### Step 5: Form the two-digit number
Now we can form the two-digit number using \( x \) and \( y \):
The number is \( 10x + y = 10 \times 2 + 6 = 20 + 6 = 26 \).

### Final Answer
The two-digit number is **26**.

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