The sum of two numbers is 30. Their difference is 6. What are the numbers?

To find the two numbers, we can set up a couple of equations based on the information given.

Let’s call the two numbers x and y.

• From the first statement, we know that the sum of the two numbers is 30:
  x + y = 30
• From the second statement, we know that their difference is 6:
  x – y = 6

Now we have a system of two equations:

1. x + y = 30
2. x – y = 6

We can solve these equations step by step. First, let’s solve for x in the second equation:

x = y + 6

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

(y + 6) + y = 30

This simplifies to:

2y + 6 = 30

Next, we subtract 6 from both sides:

2y = 24

Now, divide both sides by 2:

y = 12

Now that we have y, we can find x using our equation for x:

x = 12 + 6 = 18

So, we have found that the two numbers are:

• x = 18
• y = 12

To double-check, we can verify:

• Sum: 18 + 12 = 30
• Difference: 18 – 12 = 6

Both conditions are satisfied, so the two numbers are indeed 18 and 12.