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In 2007, the arithmetic mean of the annual incomes of Jack and Jill

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Bunuel
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In 2007, the arithmetic mean of the annual incomes of Jack and Jill [#permalink] New post   19 Apr 2024, 01:30
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­In 2007, the arithmetic mean of the annual incomes of Jack and Jill was $3800. The arithmetic mean of the annual incomes of Jill and Jess was $4800, and the arithmetic mean of the annual incomes of Jess and Jack was $5800. What is the arithmetic mean of the incomes of the three?

(A) $4000
(B) $4200
(C) $4400
(D) $4800
(E) $5000


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sayan640
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In 2007, the arithmetic mean of the annual incomes of Jack and Jill [#permalink] New post   19 Apr 2024, 05:47
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D should be the answer .  3800 + 48 00 + 58 00 = 14400/3 = 4800$­
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Re: In 2007, the arithmetic mean of the annual incomes of Jack and Jill [#permalink] New post   19 Apr 2024, 07:31
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­Let Jack = x; Jill = y and Jess = z.

Arithmetic mean of the annual incomes of Jack and Jill was $3800: \(\frac{x+y}{2}=3800\)

The arithmetic mean of the annual incomes of Jill and Jess was $4800: \(\frac{y+z}{2}=4800\)

The arithmetic mean of the annual incomes of Jess and Jack was $5800: \(\frac{x+z}{2}=5800\)

As we are essentially adding half values to get the total for each pairs annual income arithmetic mean (ie. \(\frac{a+b}{2}\) is the same as \(\frac{a}{2}+\frac{b}{2}\) ), adding the 3 above equations will give us the sum of their annual incomes. 

Summing the 3 equations: \(x + y + z = 14400\)

The arithmetic mean of the incomes of the three: \(\frac{14400}{3} = 4800\)


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Re: In 2007, the arithmetic mean of the annual incomes of Jack and Jill [#permalink] New post   20 Apr 2024, 23:03
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Bunuel wrote:
­In 2007, the arithmetic mean of the annual incomes of Jack and Jill was $3800. The arithmetic mean of the annual incomes of Jill and Jess was $4800, and the arithmetic mean of the annual incomes of Jess and Jack was $5800. What is the arithmetic mean of the incomes of the three?

(A) $4000
(B) $4200
(C) $4400
(D) $4800
(E) $5000


This is a PS Butler Question

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Re: In 2007, the arithmetic mean of the annual incomes of Jack and Jill [#permalink]
20 Apr 2024, 23:03
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