The Sum of Two Numbers is 83 and Their Difference is 7

The sum of two numbers is 83 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 83. In other words, x plus y equals 83 and can be written as equation A:

x + y = 83

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 = 83
7 + y + y = 83
7 + 2y = 83
2y = 76
y = 38

Now we know y is 38. Which means that we can substitute y for 38 in equation A and solve for x:

x + y = 83
x + 38 = 83
X = 45

Summary: The sum of two numbers is 83 and their difference is 7. What are the two numbers? Answer: 45 and 38 as proven here:

Sum: 45 + 38 = 83
Difference: 45 - 38 = 7

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