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? Answer: 25 and 5 as proven here:
Sum: 25 + 5 = 30
Difference: 25 - 5 = 20
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