The Sum of Two Numbers is 50 and Their Difference is 5

The sum of two numbers is 50 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 50. In other words, x plus y equals 50 and can be written as equation A:

x + y = 50

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 = 50
5 + y + y = 50
5 + 2y = 50
2y = 45
y = 22.5

Now we know y is 22.5. Which means that we can substitute y for 22.5 in equation A and solve for x:

x + y = 50
x + 22.5 = 50
X = 27.5

Summary: The sum of two numbers is 50 and their difference is 5. What are the two numbers? Answer: 27.5 and 22.5 as proven here:

Sum: 27.5 + 22.5 = 50
Difference: 27.5 - 22.5 = 5

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