What are the two numbers if the sum is 21 and the difference is 5?

To solve the problem, we need to set up a couple of equations based on the information given. Let’s denote the two numbers as x and y.

From the question, we have the following two equations:

• x + y = 21 (the sum of the two numbers)
• x – y = 5 (the difference of the two numbers)

Now, we can solve these equations step by step. First, we can solve for x in the second equation:

x = y + 5

Now, we can substitute this expression for x into the first equation:

(y + 5) + y = 21

Combining like terms gives us:

2y + 5 = 21

Next, we can isolate 2y by subtracting 5 from both sides:

2y = 21 - 5

2y = 16

Now, dividing both sides by 2, we find:

y = 8

Now that we have the value of y, we can substitute it back into the equation for x:

x = y + 5

x = 8 + 5

x = 13

Therefore, the two numbers are 13 and 8.

This solution can be verified by checking both the sum and the difference:

• Sum: 13 + 8 = 21
• Difference: 13 – 8 = 5

Indeed, both conditions are satisfied, confirming that the numbers are correctly found.