The Sum of Two Numbers is 1 and Their Difference is 99

The sum of two numbers is 1 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 1. In other words, x plus y equals 1 and can be written as equation A:

x + y = 1

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 = 1
99 + y + y = 1
99 + 2y = 1
2y = -98
y = -49

Now we know y is -49. Which means that we can substitute y for -49 in equation A and solve for x:

x + y = 1
x + -49 = 1
X = 50

Summary: The sum of two numbers is 1 and their difference is 99. What are the two numbers? Answer: 50 and -49 as proven here:

Sum: 50 + -49 = 1
Difference: 50 - -49 = 99

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