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

The sum of two numbers is 31 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 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 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 = 31
7 + y + y = 31
7 + 2y = 31
2y = 24
y = 12

Now we know y is 12. Which means that we can substitute y for 12 in equation A and solve for x:

x + y = 31
x + 12 = 31
X = 19

Summary: The sum of two numbers is 31 and their difference is 7. What are the two numbers? Answer: 19 and 12 as proven here:

Sum: 19 + 12 = 31
Difference: 19 - 12 = 7

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