the average of a set of six integers is 38. when a seventh number is included in the set, the average of the set increase to 47. what is the seventh number? helpppp
6*38 = 228
(228 + x )/7 = 47
228 + x = 329
x = 101
check
228 + 101 = 329
329/7 = 47 sure enough
If the average of six integers is 38, then the total must be 6 × 38, or 228. If the average of seven integers is 47, then the total must be 7 × 47, or 329. Since you are adding a seventh integer to the set, the value of the seventh integer will be the difference between 329 and 228: 329 −228 = 101.
To find the seventh number, we can start by finding the sum of the six integers in the original set. Since the average of the set is 38, the sum of the six numbers would be 6 multiplied by 38, which equals 228.
Next, we need to find the sum of the seven numbers in the updated set. We know that the average of the set with the seventh number is 47. Since the average is the sum of all the numbers divided by the count of numbers, the sum of the seven numbers would be 7 multiplied by 47, which equals 329.
Now, we can find the seventh number by subtracting the sum of the original set (228) from the sum of the updated set (329). So, the seventh number would be 329 - 228 = 101.
Therefore, the seventh number is 101.