The average (arithmetic mean) of the numbers v, w, x, y, and z is j, and the average of the numbers x, y, and z is k. What is the average of v and w in terms of j and k ?A. (j – k) / 2B. (j + k) / 2C. (5j – 3k) / 3D. (5j – 3k) / 2E. (5j – k) / 2
Question
The average (arithmetic mean) of the numbers v, w, x, y, and z is j, and the average of the numbers x, y, and z is k. What is the average of v and w in terms of j and k ?A. (j – k) / 2B. (j + k) / 2C. (5j – 3k) / 3D. (5j – 3k) / 2E. (5j – k) / 2
Solution
The problem can be solved by using the formula for the arithmetic mean (average), which is the sum of the numbers divided by the count of the numbers.
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The average of v, w, x, y, and z is j. This can be written as (v + w + x + y + z) / 5 = j. Multiplying both sides by 5 to get rid of the denominator, we get v + w + x + y + z = 5j.
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The average of x, y, and z is k. This can be written as (x + y + z) / 3 = k. Multiplying both sides by 3 to get rid of the denominator, we get x + y + z = 3k.
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We want to find the average of v and w. We can do this by subtracting the second equation from the first to get v + w = 5j - 3k.
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To find the average of v and w, we divide this by 2, so the average of v and w is (5j - 3k) / 2.
So, the answer is D. (5j – 3k) / 2.
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