The average of three numbers is 51. The second number is twice the first number, and the third number is three more than the second number. Find the average of 1st two numbers.
Question
The average of three numbers is 51. The second number is twice the first number, and the third number is three more than the second number. Find the average of 1st two numbers.
Solution
Sure, let's solve this step by step:
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We know that the average of three numbers is 51. The average is calculated by adding all the numbers and dividing by the count of numbers. So, the sum of the three numbers is 51 * 3 = 153.
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The problem states that the second number is twice the first number. If we denote the first number as x, then the second number is 2x.
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The third number is three more than the second number, so it's 2x + 3.
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Now we know that the sum of the three numbers is x + 2x + 2x + 3 = 153. Simplifying the left side gives 5x + 3 = 153.
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Solving for x, we subtract 3 from both sides to get 5x = 150, then divide by 5 to get x = 30. So, the first number is 30, the second number is 2 * 30 = 60.
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The average of the first two numbers is (30 + 60) / 2 = 45.
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