Sum of two numbers is 80 and their difference is 36. Find the numbers.

Options

A. 58, 22
B. 40,40
C. 44, 36
D. 52, 28

Answer

To solve the problem, we need to find two numbers based on the given conditions:

1. The sum of two numbers is 80.
2. The difference of the two numbers is 36.

Let's denote the two numbers as \( x \) and \( y \).

### Step 1: Set up the equations
From the problem statement, we can create the following equations:
1. \( x + y = 80 \) (Equation 1)
2. \( x - y = 36 \) (Equation 2)

### Step 2: Solve the equations
We can solve these equations using the elimination method.

First, we will add both equations (Equation 1 and Equation 2):

\[ (x + y) + (x - y) = 80 + 36 \]

This simplifies to:

\[ 2x = 116 \]

### Step 3: Find the value of \( x \)
Now, we can solve for \( x \):

\[ x = \frac{116}{2} = 58 \]

### Step 4: Substitute \( x \) back to find \( y \)
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):

\[ 58 + y = 80 \]

Subtracting 58 from both sides gives us:

\[ y = 80 - 58 = 22 \]

### Conclusion
The two numbers are:
- \( x = 58 \)
- \( y = 22 \)

### Summary
The two numbers are 58 and 22.

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