The sum of two number is 25. One of the numbers exceeds the other by 9. The number are ?

Options

A. 15,10
B. 16,9
C. 13,12
D. 17,8

Answer

To solve the problem step by step, let's denote the two numbers as \( x \) and \( y \).

### Step 1: Set up the equations
We know from the problem that:
1. The sum of the two numbers is 25:
\[ x + y = 25 \quad \text{(Equation 1)} \]
2. One number exceeds the other by 9:
\[ x = y + 9 \quad \text{(Equation 2)} \]

### Step 2: Substitute Equation 2 into Equation 1
Now, we can substitute Equation 2 into Equation 1. Replace \( x \) in Equation 1 with \( y + 9 \):
\[ (y + 9) + y = 25 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 2y + 9 = 25 \]

### Step 4: Solve for \( y \)
Subtract 9 from both sides:
\[ 2y = 25 - 9 \]
\[ 2y = 16 \]
Now, divide by 2:
\[ y = \frac{16}{2} = 8 \]

### Step 5: Find \( x \)
Now that we have \( y \), we can find \( x \) using Equation 2:
\[ x = y + 9 = 8 + 9 = 17 \]

### Conclusion
The two numbers are:
\[ x = 17 \quad \text{and} \quad y = 8 \]

### Final Answer
The numbers are 17 and 8.

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