The Sum of Two Numbers is 31 and Their Difference is 6

The sum of two numbers is 31 and their difference is 6. 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 31. In other words, x plus y equals 31 and can be written as equation A:

x + y = 31

The difference between x and y is 6. In other words, x minus y equals 6 and can be written as equation B:

x - y = 6

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

x - y = 6
x = 6 + y

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

x + y = 31
6 + y + y = 31
6 + 2y = 31
2y = 25
y = 12.5

Now we know y is 12.5. Which means that we can substitute y for 12.5 in equation A and solve for x:

x + y = 31
x + 12.5 = 31
X = 18.5

Summary: The sum of two numbers is 31 and their difference is 6. What are the two numbers? Answer: 18.5 and 12.5 as proven here:

Sum: 18.5 + 12.5 = 31
Difference: 18.5 - 12.5 = 6

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The Sum of Two Numbers is 31 and Their Difference is 7
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