Problem Solving

amandadavis wrote:the sum of three consecutive integers is greater then 57. find the smallest integers for whitch this is possible.

There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}
----------------------------------------------------
Now onto the solution...

Let's see what happens IF the SUM of the 3 integers EQUALED 57.
57/3 = 19, so the 3 integers have a mean (average) value of 19.

Since three consecutive integers are EQUALLY spaced, the mean and median are equal.
So, the MEDIAN of the 3 values is 19
So, the 3 integers are 18, 19, 20

Of course, these WOULD be the 3 integers IF their sum EQUALED 57
Since the sum is GREATER THAN 57, the next 3 integers must be three values.
So, the 3 integers are 19, 20, 21

Cheers,
Brent

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.