The average (arithmetic mean) of 6 integers is 32. If the numbers are all different, & if none is less than 10, what is the greatest possible value...

In order to find the greatest possible value of the highest number, we must consider the lowest possible values of five of the numbers. We are given the information that all the numbers are different and none are less than 10. So the lowest possible five numbers we can use are 10, 11, 12, 13, and 14. We will call the sixth number x. So we can set up an equation for the average like...

In order to find the greatest possible value of the highest number, we must consider the lowest possible values of five of the numbers. We are given the information that all the numbers are different and none are less than 10. So the lowest possible five numbers we can use are 10, 11, 12, 13, and 14. We will call the sixth number x. So we can set up an equation for the average like so:

`(10+11+12+13+14+x)/6=32`

Next we can simplify and solve for x:

`(60+x)/6=32`

`60+x=192`

`x=132`

So the largest possible value of the highest number is 132.