Answer is 11

If the average of the five numbers is 8, then the sum of those five numbers is 5 × 8, or 40. Subtract the sum of the two known numbers, 7, from 40. The sum of the other three numbers is 33.

The simplest set of 5 numbers whose average is 8 is 8, 8, 8, 8, and 8. Replacing one of the 8's with 2 drops the total by 6, and replacing another with 5 drops the total still further by 3. The total of the five numbers must be increased by 9 (since 6 + 3 = 9), so each of the three remaining 8's must be increased by 3 (three 3's = 9). That means the numbers are 2, 5, and three 11's. The value of any one of the three equal numbers is 11.

**METHOD 1:***Strategy: Find the sum of the five numbers.*If the average of the five numbers is 8, then the sum of those five numbers is 5 × 8, or 40. Subtract the sum of the two known numbers, 7, from 40. The sum of the other three numbers is 33.

**The value of any one of the three equal numbers is**33 ÷ 3, or**11.****METHOD 2:***Strategy: Start with all equal.*The simplest set of 5 numbers whose average is 8 is 8, 8, 8, 8, and 8. Replacing one of the 8's with 2 drops the total by 6, and replacing another with 5 drops the total still further by 3. The total of the five numbers must be increased by 9 (since 6 + 3 = 9), so each of the three remaining 8's must be increased by 3 (three 3's = 9). That means the numbers are 2, 5, and three 11's. The value of any one of the three equal numbers is 11.

*FOLLOW-UPS: The average of five different natural numbers is 8. Consider the largest of these numbers.(1)What is its largest possible value? [30]*

(2) What is its smallest possible value? [10](2) What is its smallest possible value? [10]