The Sum of Two Numbers is 5 and Their Difference is 99

The sum of two numbers is 5 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 5. In other words, x plus y equals 5 and can be written as equation A:

x + y = 5

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 = 5
99 + y + y = 5
99 + 2y = 5
2y = -94
y = -47

Now we know y is -47. Which means that we can substitute y for -47 in equation A and solve for x:

x + y = 5
x + -47 = 5
X = 52

Summary: The sum of two numbers is 5 and their difference is 99. What are the two numbers? Answer: 52 and -47 as proven here:

Sum: 52 + -47 = 5
Difference: 52 - -47 = 99

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