amandadavis wrote:the sum of three consecutive integers is greater then 57. find the smallest integers for whitch this is possible.
Solution:
To solve this problem we can get the "3 consecutive integers" in terms of the same variable.
Remember, consecutive integers are integers that follow each other in order such that the difference between any integer and the integer that precedes it is 1.
For example, 2, 3, 4, and 5 are four consecutive integers just as 55, 56, 57, 58, and 59 are five consecutive integers. When working with consecutive integers, it's helpful to let the first integer be represented by the variable x. From here, all of the other consecutive integers can be expressed relative to x.
So for this problem, Integer 1 = x, Integer 2 = (x + 1), and Integer 3 = (x + 2).
Since we are given that the sum of three consecutive integers is
greater than 57, we can set up an inequality to determine what x must be greater than.
x + x + 1 + x + 2 > 57
3x + 3 > 57
3x > 54
x > 18
Since x is greater than 18, the
smallest integer that would make this possible is 19. Thus the 3 consecutive integers would be 19, 20, and 21.
