Find four consecutive integers with a sum of 66

Answer 1

Consecutive integers are integers that are in order and are one away from each other. Each number is one more than the previous number. So for example, the numbers: 3, 4, 5, and 6 are all consecutive. In this example, the sum of these four consecutive numbers would be 3+4+5+6 = 18

For this particular problem, assume that the first number in this sequence is X. Then the second number is X+1, the third number is X+2, and the fourth is X+3. Together, these four numbers must equal 66. We can set this problem up as the following equation and solve to figure out what the four numbers must be:

X + (X+1) + (X+2) + (X+3) = 66

Combine like terms by summing the X values together and the constants:

4X + 1 + 2 + 3 = 66

4X + 6 = 66

Subtract 6 from both sides:

4X = 60

Divide both sides by 4:

X = 15

This means the first number in the sequence of consecutive numbers is 15. So the four consecutive integers that sum to 66 are then: 15, 16, 17, and 18.