Average of 9 numbers is 79. The average of first 2 numbers is 75 while the average of next 4 is 87. If the 8th number is 5 more than the seventh and 1 more than the ninth number, find the ninth number?

Sure, let's break it down:

1. The average of 9 numbers is 79. This means the total sum of these 9 numbers is 79 * 9 = 711.

2. The average of the first 2 numbers is 75, so the sum of these 2 numbers is 75 * 2 = 150.

3. The average of the next 4 numbers is 87, so the sum of these 4 numbers is 87 * 4 = 348.

4. Now, if we subtract the sum of the first 6 numbers (150 + 348 = 498) from the total sum of the 9 numbers (711), we get the sum of the last 3 numbers, which is 711 - 498 = 213.

5. We know that the 8th number is 5 more than the 7th and 1 more than the 9th number. Let's denote the 7th number as x. This means the 8th number is x + 5 and the 9th number is x + 5 - 1 = x + 4.

6. Since the sum of the last 3 numbers is 213, we can write the equation: x + (x + 5) + (x + 4) = 213.

7. Solving this equation gives: 3x + 9 = 213, then 3x = 204, and finally x = 68.

8. Therefore, the 9th number, which is x + 4, is 68 + 4 = 72.