Final answer:
To find the average of x + 6, y - 3, and 10, we calculate the new sum based on the changes from the original average and numbers provided. After adjustments, the new sum is 81, and dividing by the number of terms gives us an average of 27.
Step-by-step explanation:
If the average of x, y, and 4 is 24, we first want to find the sum of these three numbers. To find the sum, we multiply the average, which is 24, by the number of terms, which is 3 (since we have three numbers: x, y, and 4). This gives us:
24 × 3 = 72, so x + y + 4 = 72.
Next, we want to find the average of x + 6, y - 3, and 10. To do this, we consider that we are adding 6 to x and subtracting 3 from y, with an overall net change of 6 - 3 = 3 added to the original sum. Since 4 is replaced by 10, we have an additional change of 10 - 4 = 6. The new sum becomes:
72 (original sum) + 3 (change from x and y) + 6 (change from replacing 4 with 10) = 81.
Now, we divide this sum by the number of terms, which is still 3, to find the new average:
81 ÷ 3 = 27.
Therefore, the average of x + 6, y - 3, and 10 is 27.