The sum of four consecutive number is 34. What are these numbers

Answer: The four numbers are $7$ , $8$ , $9$ , and $10$ .

Step-by-step solution

Step 1: Define the consecutive numbers in terms of a variable

Let the first integer be $x$ . Since consecutive integers increase by $1$ each time, the next three consecutive integers are $x + 1$ , $x + 2$ , and $x + 3$ .

Step 2: Set up the equation using the given sum

We are given that the sum of these four consecutive integers is equal to $34$ . Combining like terms gives $4x + 6 = 34$ .

Step 3: Solve the linear equation for $x$

Subtract $6$ from both sides of the equation to isolate the term with $x$ , giving $4x = 28$ . Then divide both sides by $4$ to find $x = 7$ .

Step 4: Determine the four consecutive numbers

Substitute $x = 7$ back into each of our expressions to find the four numbers: $7$ , $8$ , $9$ , and $10$ . We can verify by adding them: $7 + 8 + 9 + 10 = 34$ .

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