The difference between two numbers is 26 and the larger number exceeds thrice of the smaller number by 4. Find the numbers.

Options

A. 38,12
B. 40,14
C. 37,11
D. none of these

Answer

To solve the problem step by step, we will define the two numbers and set up equations based on the information given.

### Step 1: Define the Variables
Let the larger number be \( x \) and the smaller number be \( y \). According to the problem, we know that:
- The larger number exceeds the smaller number.
- Therefore, we can write:
\[ x > y \]

### Step 2: Set Up the First Equation
The problem states that the difference between the two numbers is 26. This can be expressed as:
\[ x - y = 26 \]
(Equation 1)

### Step 3: Set Up the Second Equation
The problem also states that the larger number exceeds thrice the smaller number by 4. This can be expressed as:
\[ x - 3y = 4 \]
(Equation 2)

### Step 4: Solve the Equations
Now we have a system of two equations:
1. \( x - y = 26 \)
2. \( x - 3y = 4 \)

We can solve these equations simultaneously. Let's start by solving Equation 1 for \( x \):
\[ x = y + 26 \]

### Step 5: Substitute into the Second Equation
Now, substitute \( x \) from Equation 1 into Equation 2:
\[ (y + 26) - 3y = 4 \]
This simplifies to:
\[ y + 26 - 3y = 4 \]
\[ -2y + 26 = 4 \]

### Step 6: Isolate \( y \)
Now, isolate \( y \):
\[ -2y = 4 - 26 \]
\[ -2y = -22 \]
\[ y = \frac{-22}{-2} = 11 \]

### Step 7: Find \( x \)
Now that we have \( y \), we can find \( x \) using Equation 1:
\[ x = y + 26 \]
\[ x = 11 + 26 = 37 \]

### Conclusion
The two numbers are:
- Larger number \( x = 37 \)
- Smaller number \( y = 11 \)

### Final Answer
The numbers are \( 37 \) and \( 11 \).

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