The Sum of Two Numbers is 30 and Their Difference is 5

The sum of two numbers is 30 and their difference is 5. 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 5. In other words, x minus y equals 5 and can be written as equation B:

x - y = 5

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

x - y = 5
x = 5 + y

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

x + y = 30
5 + y + y = 30
5 + 2y = 30
2y = 25
y = 12.5

Now we know y is 12.5. Which means that we can substitute y for 12.5 in equation A and solve for x:

x + y = 30
x + 12.5 = 30
X = 17.5

Summary: The sum of two numbers is 30 and their difference is 5. What are the two numbers? Answer: 17.5 and 12.5 as proven here:

Sum: 17.5 + 12.5 = 30
Difference: 17.5 - 12.5 = 5

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