The Sum of Two Numbers is 75 and Their Difference is 5

The sum of two numbers is 75 and their difference is 5. 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 75. In other words, x plus y equals 75 and can be written as equation A:

x + y = 75

The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:

x - y = 5

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

x - y = 5
x = 5 + y

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

x + y = 75
5 + y + y = 75
5 + 2y = 75
2y = 70
y = 35

Now we know y is 35. Which means that we can substitute y for 35 in equation A and solve for x:

x + y = 75
x + 35 = 75
X = 40

Summary: The sum of two numbers is 75 and their difference is 5. What are the two numbers? Answer: 40 and 35 as proven here:

Sum: 40 + 35 = 75
Difference: 40 - 35 = 5

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