The Sum of Two Numbers is 52 and Their Difference is 5

The sum of two numbers is 52 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 52. In other words, x plus y equals 52 and can be written as equation A:

x + y = 52

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 = 52
5 + y + y = 52
5 + 2y = 52
2y = 47
y = 23.5

Now we know y is 23.5. Which means that we can substitute y for 23.5 in equation A and solve for x:

x + y = 52
x + 23.5 = 52
X = 28.5

Summary: The sum of two numbers is 52 and their difference is 5. What are the two numbers? Answer: 28.5 and 23.5 as proven here:

Sum: 28.5 + 23.5 = 52
Difference: 28.5 - 23.5 = 5

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