The Sum of Two Numbers is 51 and Their Difference is 8

The sum of two numbers is 51 and their difference is 8. 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 51. In other words, x plus y equals 51 and can be written as equation A:

x + y = 51

The difference between x and y is 8. In other words, x minus y equals 8 and can be written as equation B:

x - y = 8

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

x - y = 8
x = 8 + y

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

x + y = 51
8 + y + y = 51
8 + 2y = 51
2y = 43
y = 21.5

Now we know y is 21.5. Which means that we can substitute y for 21.5 in equation A and solve for x:

x + y = 51
x + 21.5 = 51
X = 29.5

Summary: The sum of two numbers is 51 and their difference is 8. What are the two numbers? Answer: 29.5 and 21.5 as proven here:

Sum: 29.5 + 21.5 = 51
Difference: 29.5 - 21.5 = 8

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The Sum of Two Numbers is 51 and Their Difference is 9
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