The sum of two numbers is 30 and their difference is 20. What are the two numbers?

Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 30. In other words, x plus y equals 30 and can be written as equation A:

x + y = 30

The difference between x and y is 20. In other words, x minus y equals 20 and can be written as equation B:

x - y = 20

Now solve equation B for x to get the revised equation B:

x - y = 20

x = 20 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 30

20 + y + y = 30

20 + 2y = 30

2y = 10

y = 5

Now we know y is 5. Which means that we can substitute y for 5 in equation A and solve for x:

x + y = 30

x + 5 = 30

X = 25

Summary: The sum of two numbers is 30 and their difference is 20. What are the two numbers? 25 and 5 as proven here:

Sum: 25 + 5 = 30

Difference: 25 - 5 = 20

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