The Sum of Two Numbers is 31 and Their Difference is 99

The sum of two numbers is 31 and their difference is 99. 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 99. In other words, x minus y equals 99 and can be written as equation B:

x - y = 99

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

x - y = 99
x = 99 + y

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

x + y = 31
99 + y + y = 31
99 + 2y = 31
2y = -68
y = -34

Now we know y is -34. Which means that we can substitute y for -34 in equation A and solve for x:

x + y = 31
x + -34 = 31
X = 65

Summary: The sum of two numbers is 31 and their difference is 99. What are the two numbers? Answer: 65 and -34 as proven here:

Sum: 65 + -34 = 31
Difference: 65 - -34 = 99

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