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The sum of three consecutive even integers is one hundred seventy-four. Find the first number

To solve the problem of finding the first of three consecutive even integers whose sum is 174, we can set up the following equation:

Let the first even integer be \( x \). Then, the next two consecutive even integers will be \( x + 2 \) and \( x + 4 \).

The sum of these three integers is:

\[ x + (x + 2) + (x + 4) = 174 \]

Combining like terms, we get:

\[ 3x + 6 = 174 \]

To solve for \( x \), first subtract 6 from both sides:

\[ 3x = 168 \]

Then, divide both sides by 3:

\[ x = 56 \]

Thus, the first number is **56**.

Discover how to find the first number of three consecutive even integers that add up to 174. This problem involves arithmetic sequences and linear equations, suitable for Grades 7-9 students.

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