The average of 6 numbers is 5x10^6. The average of the first 5 numbers is 6x10^6. What is the last number?
***PLEASE, I only want to know HOW to do it, NOT the answer.***
Thank you!
***PLEASE, I only want to know HOW to do it, NOT the answer.***
Thank you!
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Well, we know that the average of 6 numbers to take the sum and divide it by 6. Conversely, we could figure out the sum by multiplying the average by 6. If the average of 6 numbers was 5, then we can conclude that the sum was, 30. Then, for the second one, if the average of the first 5 numbers was 4, we can conclude that the sum is 20, and conclude that the last number is 10. We just apply this principle by making both sides equal, and adding a variable.
(5x10^6)6 = (6x10^6)5 + y
30x10^6 = 30x10^6 + y
0 = y
(5x10^6)6 = (6x10^6)5 + y
30x10^6 = 30x10^6 + y
0 = y
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Figure it on the basis of the weighted average:
(5/6)(6x10^6) + 1/6(x) = 5x10^6
The weight of the first five numbers' average is 5/6 of the final average. The last number contributes 1/6 of the total.
Multiply through by 6 to clear the fractions:
5(6x10^6) + x = 30x10^6
Subtract the 5(6x10^6) from both sides to calculate x.
(5/6)(6x10^6) + 1/6(x) = 5x10^6
The weight of the first five numbers' average is 5/6 of the final average. The last number contributes 1/6 of the total.
Multiply through by 6 to clear the fractions:
5(6x10^6) + x = 30x10^6
Subtract the 5(6x10^6) from both sides to calculate x.
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find the sum of the first 5 numbers (5 * the average)
find the sum of the first 6 numbers (6 * the average)
the difference is the last number
find the sum of the first 6 numbers (6 * the average)
the difference is the last number
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If its easy why do you need help? Trolololol