If the sum of two numbers is 100 and the bigger number is 28 more than the smaller number, find the two numbers.

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 smaller number be \( x \) and the bigger number be \( y \).

### Step 2: Set up the equations
From the problem, we know:
1. The sum of the two numbers is 100:
\[ x + y = 100 \]
2. The bigger number is 28 more than the smaller number:
\[ y = x + 28 \]

### Step 3: Substitute the second equation into the first equation
We can substitute \( y \) from the second equation into the first equation:
\[ x + (x + 28) = 100 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 2x + 28 = 100 \]

### Step 5: Solve for \( x \)
Subtract 28 from both sides:
\[ 2x = 100 - 28 \]
\[ 2x = 72 \]
Now, divide both sides by 2:
\[ x = \frac{72}{2} \]
\[ x = 36 \]

### Step 6: Find \( y \)
Now that we have \( x \), we can find \( y \) using the equation \( y = x + 28 \):
\[ y = 36 + 28 \]
\[ y = 64 \]

### Conclusion
The two numbers are:
- Smaller number \( x = 36 \)
- Bigger number \( y = 64 \)

### Final Answer
The two numbers are 36 and 64.

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