Some equations are based on the basis of a certain system. Using the same solve the unsolved equation.
If 10 - 3 = 12, 12 - 4 = 13,
14 -5 = 14, what is 16 -6?

Options

A. 10
B. 15
C. 16
D. 18

Explanation

To solve the equation based on the given pattern, let's analyze the provided equations step by step.

### Given Equations:
1. \( 10 - 3 = 12 \)
2. \( 12 - 4 = 13 \)
3. \( 14 - 5 = 14 \)

### Step 1: Analyze the First Equation
For the equation \( 10 - 3 = 12 \):
- First, we add the two numbers:
\[ 10 + 3 = 13 \]
- Next, we find the sum of the digits of the first number (10):
\[ 1 + 0 = 1 \]
- Now, we subtract this sum from the previous result:
\[ 13 - 1 = 12 \]
Thus, the equation holds true.

### Step 2: Analyze the Second Equation
For the equation \( 12 - 4 = 13 \):
- Add the two numbers:
\[ 12 + 4 = 16 \]
- Find the sum of the digits of the first number (12):
\[ 1 + 2 = 3 \]
- Now, subtract this sum from the previous result:
\[ 16 - 3 = 13 \]
Thus, this equation also holds true.

### Step 3: Analyze the Third Equation
For the equation \( 14 - 5 = 14 \):
- Add the two numbers:
\[ 14 + 5 = 19 \]
- Find the sum of the digits of the first number (14):
\[ 1 + 4 = 5 \]
- Now, subtract this sum from the previous result:
\[ 19 - 5 = 14 \]
Thus, this equation holds true as well.

### Step 4: Solve the Unsolved Equation \( 16 - 6 \)
Now, we need to solve \( 16 - 6 \):
- First, add the two numbers:
\[ 16 + 6 = 22 \]
- Next, find the sum of the digits of the first number (16):
\[ 1 + 6 = 7 \]
- Now, subtract this sum from the previous result:
\[ 22 - 7 = 15 \]

### Final Answer:
Thus, \( 16 - 6 = 15 \).

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