using equation to solve word problems

Question

the sum of four consecutive integers is 222. find the integers.

Answer 1

If they are consecutive, then each one is 1 away from the previous one. To solve this problem, we look at our initial term as x, and then consider how far each of the other three terms are from the first one.

Our 4 consecutive integers are going to be

x

x + 1

x + 2

x + 3

So add them all together

x + x + 1 + x + 2 + x + 3 = 222

Combine like terms:

4x + 6 = 222

Subtract 6 from each side:

4x = 216

Divide by 4:

x = 54

So the integers are:

54

55

56

57

Answer 2

This problem hinges on the word consecutive. If we say that n is the first integer, then the next integer would be n + 1, the next would be n + 2, and the next would be n + 3. Thus the sum of four consecutive integers would be

n + (n + 1) + (n + 2) + (n + 3)

We want this sum to be 222 and therefore we are looking to solve

n + (n + 1) + (n + 2) + (n + 3) = 222

4n + 6 = 222

4n = 216

n = 54.

Thus the integers are n = 54, n + 1 = 55, n + 2 = 56, and n + 3 = 57.