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?
(6(38) + x)/7 = 47
228 + x = 329
x = 101
101 was added as the 7th number
Well, well, well! Looks like we have a numbers party going on here! Let's solve this math mystery, shall we?
Alright, so the average of the first six integers is 38. If we multiply 38 by 6, we get the sum of those six numbers, which is 228, right?
Now, when a seventh number joins the party, the average increases to 47. To find the sum of the seven numbers, we multiply 47 by 7, which gives us 329.
To determine the seventh number, we need to subtract the sum of the first six numbers (228) from the sum of all seven numbers (329). Are you ready for this drumroll, please?
🥁 The seventh number is 101! 🎉
So, we kicked up the average by adding 101 to the party, and now everything is peaches and averages!
To find the seventh number, we can start by calculating the sum of the original six integers. Since the average of the set is 38, we can multiply the average by the number of integers to find the sum: 38 * 6 = 228.
Next, we need to find the sum of the seventh number and the sum of the original six integers. We know that when the seventh number is included, the average increases to 47. Since the average is the sum divided by the number of elements, we can calculate the sum by multiplying the average by the total number of elements in the set: 47 * 7 = 329.
Finally, we can find the seventh number by subtracting the sum of the original six integers from the sum of the entire set: 329 - 228 = 101.
Therefore, the seventh number is 101.
To find the seventh number, we can follow these steps:
Step 1: Find the sum of the original six integers.
Since the average of the six integers is 38, the sum of the six numbers can be found by multiplying the average by the number of elements: 38 * 6 = 228.
Step 2: Find the sum of the new set with the seventh number.
Since the average of the new set, including the seventh number, is 47, the sum of the entire set can be found by multiplying the new average by the new number of elements: 47 * 7 = 329.
Step 3: Find the seventh number.
The difference between the sum of the new set and the sum of the original set will give us the value of the seventh number: 329 - 228 = 101.
Therefore, the seventh number is 101.