The Sum of Two Numbers is 17 and Their Difference is 7

The sum of two numbers is 17 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 17. In other words, x plus y equals 17 and can be written as equation A:

x + y = 17

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 = 17
7 + y + y = 17
7 + 2y = 17
2y = 10
y = 5

Now we know y is 5. Which means that we can substitute y for 5 in equation A and solve for x:

x + y = 17
x + 5 = 17
X = 12

Summary: The sum of two numbers is 17 and their difference is 7. What are the two numbers? Answer: 12 and 5 as proven here:

Sum: 12 + 5 = 17
Difference: 12 - 5 = 7

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