The Sum of Two Numbers is 3 and Their Difference is 99

The sum of two numbers is 3 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 3. In other words, x plus y equals 3 and can be written as equation A:

x + y = 3

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 = 3
99 + y + y = 3
99 + 2y = 3
2y = -96
y = -48

Now we know y is -48. Which means that we can substitute y for -48 in equation A and solve for x:

x + y = 3
x + -48 = 3
X = 51

Summary: The sum of two numbers is 3 and their difference is 99. What are the two numbers? Answer: 51 and -48 as proven here:

Sum: 51 + -48 = 3
Difference: 51 - -48 = 99

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