The Sum of Two Numbers is 40 and Their Difference is 71

The sum of two numbers is 40 and their difference is 71. 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 40. In other words, x plus y equals 40 and can be written as equation A:

x + y = 40

The difference between x and y is 71. In other words, x minus y equals 71 and can be written as equation B:

x - y = 71

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

x - y = 71
x = 71 + y

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

x + y = 40
71 + y + y = 40
71 + 2y = 40
2y = -31
y = -15.5

Now we know y is -15.5. Which means that we can substitute y for -15.5 in equation A and solve for x:

x + y = 40
x + -15.5 = 40
X = 55.5

Summary: The sum of two numbers is 40 and their difference is 71. What are the two numbers? Answer: 55.5 and -15.5 as proven here:

Sum: 55.5 + -15.5 = 40
Difference: 55.5 - -15.5 = 71

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The Sum of Two Numbers is 40 and Their Difference is 72
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