The Sum of Two Numbers is 82 and Their Difference is 7

The sum of two numbers is 82 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 82. In other words, x plus y equals 82 and can be written as equation A:

x + y = 82

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 = 82
7 + y + y = 82
7 + 2y = 82
2y = 75
y = 37.5

Now we know y is 37.5. Which means that we can substitute y for 37.5 in equation A and solve for x:

x + y = 82
x + 37.5 = 82
X = 44.5

Summary: The sum of two numbers is 82 and their difference is 7. What are the two numbers? Answer: 44.5 and 37.5 as proven here:

Sum: 44.5 + 37.5 = 82
Difference: 44.5 - 37.5 = 7

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The Sum of Two Numbers is 82 and Their Difference is 8
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