Questions: The sum of three consecutive integers is forty-two. Find the three numbers.

The sum of three consecutive integers is forty-two. Find the three numbers.

Solution

Step 1: Define the variables

Let the three consecutive integers be: \[ x, \quad x + 1, \quad x + 2 \]

Step 2: Set up the equation

The sum of the three consecutive integers is 42: \[ x + (x + 1) + (x + 2) = 42 \]

Step 3: Simplify the equation

Combine like terms: \[ 3x + 3 = 42 \]

Step 4: Solve for \(x\)

Subtract 3 from both sides: \[ 3x = 39 \] Divide both sides by 3: \[ x = 13 \]

Step 5: Find the three numbers

The three consecutive integers are: \[ x = 13, \quad x + 1 = 14, \quad x + 2 = 15 \]

The three consecutive integers are: \[ \boxed{13, \ 14, \ 15} \]

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