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In a weight-lifting competition, the average (arithmetic mean) of Pier

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In a weight-lifting competition, the average (arithmetic mean) of Pier  [#permalink]

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New post 03 Jan 2018, 21:22
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In a weight-lifting competition, the average (arithmetic mean) of Pierre's two lifts was n pounds. If the weight of his first lift was 300 less pounds than twice the weight of his second lift, what is the weight, in pounds of his first lift?

A. n/2

B. 4n/3 - 100

C. 2n/3 + 350

D. 2n/6 + 350

E. (4n + 50)/3

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Re: In a weight-lifting competition, the average (arithmetic mean) of Pier  [#permalink]

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New post 03 Jan 2018, 22:10
Average of two weights
\(L_1\) + \(L_2\) =2n -----(1)

\(L_1\) = 2\(L_2\) - 300

\(L_1\)- 2\(L_2\) = - 300 -----(2)

Multiply eq 1 with 2
2\(L_1\) + 2\(L_2\) =4n -----(3)

Adding eq no 2 and 3
3\(L_1\) = 4n-300

\(L_1\) = 4n/3-100

Ans. B
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In a weight-lifting competition, the average (arithmetic mean) of Pier  [#permalink]

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New post 03 Jan 2018, 22:40
Bunuel wrote:
In a weight-lifting competition, the average (arithmetic mean) of Pierre's two lifts was n pounds. If the weight of his first lift was 300 less pounds than twice the weight of his second lift, what is the weight, in pounds of his first lift?

A. n/2

B. 4n/3 - 100

C. 2n/3 + 350

D. 2n/6 + 350

E. (4n + 50)/3

First lift = F
Second lift = S

The average of Pierre's two lifts was \(n\)

\(\frac{F + N}{2}= n\)
\(F + S = 2n\)

His first lift was 300 less pounds than twice the weight of his second lift
--We want to solve for F
--Define S in terms of F

\(F = 2S - 300\)
\(F + 300 = 2S\)
\(2S = F + 300\)
\(S = \frac{F+300}{2}\)

Back to the equation above, substitute for S
\(F + S = 2n\)

\(F +
\frac{F+300}{2} = 2n\)

\(2F + F + 300 = 4n\)
\(3F = 4n - 300\)

\(F = \frac{4}{3}n - \frac{300}{3}\)

\(F = \frac{4}{3}n - 100\)

Answer
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Re: In a weight-lifting competition, the average (arithmetic mean) of Pier  [#permalink]

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New post 04 Jan 2018, 00:13
Smart no. works here.
Assume, second weight is 500, then first weight is 700 , and average of two weight that is 600 fits in "B".
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Re: In a weight-lifting competition, the average (arithmetic mean) of Pier   [#permalink] 04 Jan 2018, 00:13
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