The sum of two numbers is 14 and the difference is 4. What are the numbers?

Let’s denote the two numbers as x and y. From the information given, we can set up the following two equations:

• x + y = 14 (Equation 1)
• x – y = 4 (Equation 2)

To solve for x and y, we can isolate one variable in Equation 2. We can express x in terms of y:

x = y + 4

Now, we substitute this expression for x back into Equation 1:

(y + 4) + y = 14

This simplifies to:

2y + 4 = 14

Next, we subtract 4 from both sides:

2y = 10

Then, divide by 2:

y = 5

Now that we have the value of y, we can find x using the expression we derived earlier:

x = y + 4 = 5 + 4 = 9

So the two numbers are 9 and 5.

To verify, we can check both conditions:

• Sum: 9 + 5 = 14
• Difference: 9 – 5 = 4

Since both conditions hold true, we can confidently say the numbers are 9 and 5.