How can I find two numbers if their sum is 18 and their difference is 4?

To find two numbers where the sum is 18 and the difference is 4, we can set up a couple of equations based on the information provided.

Let’s denote the two numbers as x and y. We can express the conditions given in the problem as:

• Equation 1 (Sum): x + y = 18
• Equation 2 (Difference): x – y = 4

Now, we can solve these equations step by step:

1. Start with Equation 1:

x + y = 18

2. Next, reorganize Equation 2 to express one variable in terms of the other:

x = y + 4

3. Now, substitute this expression for x into Equation 1:

(y + 4) + y = 18

4. Simplifying this, we get:

2y + 4 = 18

5. Subtract 4 from both sides:

2y = 14

6. Now, divide both sides by 2:

y = 7

Now that we have the value of y, we can use it to find x:

8. Substitute y back into the equation for x:

x = y + 4 = 7 + 4

9. This gives us:

x = 11

Thus, the two numbers are:

• x = 11
• y = 7

To verify:

• Sum: 11 + 7 = 18
• Difference: 11 – 7 = 4

Both conditions hold true. Therefore, the two numbers are 11 and 7.