The Sum of Two Numbers is 81 and Their Difference is 7

The sum of two numbers is 81 and their difference is 7. 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 81. In other words, x plus y equals 81 and can be written as equation A:

x + y = 81

The difference between x and y is 7. In other words, x minus y equals 7 and can be written as equation B:

x - y = 7

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

x - y = 7
x = 7 + y

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

x + y = 81
7 + y + y = 81
7 + 2y = 81
2y = 74
y = 37

Now we know y is 37. Which means that we can substitute y for 37 in equation A and solve for x:

x + y = 81
x + 37 = 81
X = 44

Summary: The sum of two numbers is 81 and their difference is 7. What are the two numbers? Answer: 44 and 37 as proven here:

Sum: 44 + 37 = 81
Difference: 44 - 37 = 7

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