The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is:
Question
The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is:
Solution
Sure, let's solve this step by step:
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The average of six numbers is 30. Therefore, the sum of these six numbers is 30 * 6 = 180.
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The average of the first four numbers is 25. Therefore, the sum of these four numbers is 25 * 4 = 100.
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The average of the last three numbers is 35. Therefore, the sum of these three numbers is 35 * 3 = 105.
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Notice that the fourth number is counted in both the first four numbers and the last three numbers.
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If we add the sum of the first four numbers (100) and the sum of the last three numbers (105), we get 205. But we know that the sum of all six numbers is 180.
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Therefore, the fourth number, which was counted twice, is 205 - 180 = 25.
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