The Sum of Two Numbers is 23 and Their Difference is 3

The sum of two numbers is 23 and their difference is 3. 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 23. In other words, x plus y equals 23 and can be written as equation A:

x + y = 23

The difference between x and y is 3. In other words, x minus y equals 3 and can be written as equation B:

x - y = 3

Now solve equation B for x to get the revised equation B:

x - y = 3
x = 3 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 23
3 + y + y = 23
3 + 2y = 23
2y = 20
y = 10

Now we know y is 10. Which means that we can substitute y for 10 in equation A and solve for x:

x + y = 23
x + 10 = 23
X = 13

Summary: The sum of two numbers is 23 and their difference is 3. What are the two numbers? Answer: 13 and 10 as proven here:

Sum: 13 + 10 = 23
Difference: 13 - 10 = 3

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The Sum of Two Numbers is 23 and Their Difference is 4
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