What three consecutive integers have a sum of 76?

Here we will use algebra to find three consecutive integers whose sum is 76. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 76. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 76

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 76
3X + 3 = 76

3X + 3 - 3 = 76 - 3
3X = 73

3X/3 = 73/3
X = 24 1/3

Since 24 1/3 is not an integer, there is no true answer to this problem.

However, there are three numbers that add up to 76. The first number is (24 1/3), the second number is (24 1/3) + 1, and the third number is (24 1/3) + 2. Therefore, we could make this the answer to "Three consecutive numbers that add up to 76 are?":

24 1/3 + 25 1/3 + 26 1/3 = 76

Three Consecutive Integers
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What three consecutive integers have a sum of 77?
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