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Over the last three years a scientist had an average (arithmetic mean)

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Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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New post 01 Dec 2018, 08:07
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Question Stats:

60% (01:51) correct 40% (02:04) wrong based on 68 sessions

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Over the last three years a scientist had an average (arithmetic mean) yearly income of $45,000. The scientist earned \(1\frac{1}{2}\) times as much the second year as the first year and \(2\frac{1}{2}\) times as much the third year as the first year. What was the scientist's income the second year?

(A) $9,000
(B) $13,500
(e) $27,000
(D) $40,500
(E) $45,000

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Re: Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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New post 01 Dec 2018, 08:25
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Average of 3 years = 45,000$
Total income in 3 years = 135,000$

Let the income in first year be x.
Now, x+3/2x+5/x = 135,000
x = 27,000$

Income in second year = 1.5(27000) = 40,500$

D is the answer.
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Re: Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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New post 01 Dec 2018, 15:21
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Let first year salary be x
then second year salary = 1.5x
Third year = 2.5 x
Average salary for three years is 45000 which means total salary for 3 years = 45000(3)
x+1.5x+2.5x=135000
5x=135000
x=27000

Second year salary is 1.5x= 1.5*27000
=$40,500

D is the correct answer
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Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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New post 02 Dec 2018, 03:00
Average income for three months is 45000, then total income for three months is 45,000*3 = 135,000


"The scientist earned \(1\frac{1}{2}\) times as much the second year as the first year"

So,

Let First year be \(x\)

Then second Year is \(\frac{3x}{2}\)

"and \(2\frac{1}{2}\) times as much the third year as the first year"

So third Year is \(\frac{5x}{2}\)

\(\frac{X}{1} +\frac{3x}{2}+\frac{5x}{2} = 135,000\)

\(\frac{10x}{2}\) = \(135,000\)

\(10x = 270,000\)

\(x = 27,000\)

Second year = \(\frac{3}{2} * 27000 = 40,500\)


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Re: Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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New post 10 Feb 2019, 20:09
HKD1710 wrote:
Over the last three years a scientist had an average (arithmetic mean) yearly income of $45,000. The scientist earned \(1\frac{1}{2}\) times as much the second year as the first year and \(2\frac{1}{2}\) times as much the third year as the first year. What was the scientist's income the second year?

(A) $9,000
(B) $13,500
(e) $27,000
(D) $40,500
(E) $45,000



3 Years AM = 45000, Total Sum will be 135000

Given Y2 = 3/2 Y1
Y3 = 5/2 Y1

Y1 + Y2 + Y3 = 135000
substitute for above
Y1 = 27000

Y2 = 3/2 Y1 = 40500

D
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Re: Over the last three years a scientist had an average (arithmetic mean)   [#permalink] 10 Feb 2019, 20:09
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