The of the 45 numbers is 9.the average of the first 20 is 10 and the average of the last 24 is 8.find the 21st number.
I have solved please check this.
9=x/45 ,so x=415.
10=x/20, x=200
and 8=x/24, x=192
So,415-(200+192)=23.answer
Is this way and answer correct?
I will assume you meant:
The average of the 45 numbers is 9
let the sum of all 45 be x
x/45=9
x=415 <--- you had that
let the sum of the first 20 be a
a/20=10
a = 200
let the sum of the last 24 be b
b/24 = 8
b = 192
looks like the 21st number is no included, so
the 21st number is x - a - b
= 415-200-192 = 23
you had that, and your answer is correct
My only objection to your solution is your choice of the variable x to represent two different quantities
Thank you :)
Your method is incorrect, and the answer you obtained is not correct either. Let me explain how to solve the problem correctly.
Let's assign variables to the given information:
Let's assume the sum of all 45 numbers is represented by S.
The sum of the first 20 numbers is represented by F, and the sum of the last 24 numbers is represented by L.
From the given information, we can write the following equations:
1) S/45 = 9 (the average of all 45 numbers is 9)
2) F/20 = 10 (the average of the first 20 numbers is 10)
3) L/24 = 8 (the average of the last 24 numbers is 8)
To find the value of the 21st number, we need to calculate the sum of the first 20 numbers and the sum of all 45 numbers:
The sum of the first 20 numbers (F) can be found by multiplying the average (10) by the number of terms (20):
F = 10 * 20 = 200
The sum of all 45 numbers (S) can be found by multiplying the average (9) by the number of terms (45):
S = 9 * 45 = 405
Now, we can find the sum of the last 24 numbers (L) by subtracting the sum of the first 20 numbers (F) from the sum of all 45 numbers (S):
L = S - F = 405 - 200 = 205
Now, we need to find the 21st number, which is the difference between the sum of the first 21 numbers and the sum of the first 20 numbers:
21st number = (F + L) - F = L = 205
Therefore, the 21st number is 205.
To summarize, the correct solution to find the 21st number is:
1) Calculate the sum of the first 20 numbers using their average and number of terms.
2) Calculate the sum of all 45 numbers using their average and number of terms.
3) Calculate the sum of the last 24 numbers by subtracting the sum of the first 20 numbers from the sum of all 45 numbers.
4) The 21st number is equal to the sum of the last 24 numbers.
Hope this explanation helps!