The Sum of Two Numbers is 19 and Their Difference is 5

The sum of two numbers is 19 and their difference is 5. 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 19. In other words, x plus y equals 19 and can be written as equation A:

x + y = 19

The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:

x - y = 5

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

x - y = 5
x = 5 + y

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

x + y = 19
5 + y + y = 19
5 + 2y = 19
2y = 14
y = 7

Now we know y is 7. Which means that we can substitute y for 7 in equation A and solve for x:

x + y = 19
x + 7 = 19
X = 12

Summary: The sum of two numbers is 19 and their difference is 5. What are the two numbers? Answer: 12 and 7 as proven here:

Sum: 12 + 7 = 19
Difference: 12 - 7 = 5

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