The Sum of Two Numbers is 31 and Their Difference is 5

The sum of two numbers is 31 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 31. In other words, x plus y equals 31 and can be written as equation A:

x + y = 31

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 = 31
5 + y + y = 31
5 + 2y = 31
2y = 26
y = 13

Now we know y is 13. Which means that we can substitute y for 13 in equation A and solve for x:

x + y = 31
x + 13 = 31
X = 18

Summary: The sum of two numbers is 31 and their difference is 5. What are the two numbers? Answer: 18 and 13 as proven here:

Sum: 18 + 13 = 31
Difference: 18 - 13 = 5

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