The average of twelve positive numbers is 15. If the average of the first four numbers is 9 and that of the last four numbers is 26. What is the average of the remaining four numbers?
Question
The average of twelve positive numbers is 15. If the average of the first four numbers is 9 and that of the last four numbers is 26. What is the average of the remaining four numbers?
Solution 1
Sure, let's solve this step by step:
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The average of twelve numbers is 15. This means the total sum of these twelve numbers is 12 * 15 = 180.
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The average of the first four numbers is 9. This means the total sum of these four numbers is 4 * 9 = 36.
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The average of the last four numbers is 26. This means the total sum of these four numbers is 4 * 26 = 104.
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Now, to find the total sum of the remaining four numbers, we subtract the sum of the first four numbers and the last four numbers from the total sum of all twelve numbers. So, 180 - 36 - 104 = 40.
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Finally, to find the average of these remaining four numbers, we divide the total sum by 4. So, 40 / 4 = 10.
Therefore, the average of the remaining four numbers is 10.
Solution 2
Sure, let's solve this step by step:
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The average of twelve numbers is 15. This means the total sum of these twelve numbers is 12 * 15 = 180.
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The average of the first four numbers is 9. This means the total sum of these four numbers is 4 * 9 = 36.
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The average of the last four numbers is 26. This means the total sum of these four numbers is 4 * 26 = 104.
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Now, to find the total sum of the remaining four numbers, we subtract the sum of the first four numbers and the last four numbers from the total sum of twelve numbers. So, 180 - 36 - 104 = 40.
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The average of the remaining four numbers is the total sum of these numbers divided by 4. So, 40 / 4 = 10.
Therefore, the average of the remaining four numbers is 10.
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