The Sum of Two Numbers is 21 and Their Difference is 7

The sum of two numbers is 21 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 21. In other words, x plus y equals 21 and can be written as equation A:

x + y = 21

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 = 21
7 + y + y = 21
7 + 2y = 21
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 = 21
x + 7 = 21
X = 14

Summary: The sum of two numbers is 21 and their difference is 7. What are the two numbers? Answer: 14 and 7 as proven here:

Sum: 14 + 7 = 21
Difference: 14 - 7 = 7

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