The Sum of Two Numbers is 10 and Their Difference is 5

The sum of two numbers is 10 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 10. In other words, x plus y equals 10 and can be written as equation A:

x + y = 10

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 = 10
5 + y + y = 10
5 + 2y = 10
2y = 5
y = 2.5

Now we know y is 2.5. Which means that we can substitute y for 2.5 in equation A and solve for x:

x + y = 10
x + 2.5 = 10
X = 7.5

Summary: The sum of two numbers is 10 and their difference is 5. What are the two numbers? Answer: 7.5 and 2.5 as proven here:

Sum: 7.5 + 2.5 = 10
Difference: 7.5 - 2.5 = 5

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