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

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
In a weight-lifting competition, the average (arithmetic mean) of Pier  [#permalink]

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03 Jan 2018, 21:22
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25% (medium)

Question Stats:

84% (02:53) correct 16% (02:04) wrong based on 25 sessions

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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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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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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
$$F + S = 2n$$

$$F + \frac{F+300}{2} = 2n$$

$$2F + F + 300 = 4n$$
$$3F = 4n - 300$$

$$F = \frac{4}{3}n - \frac{300}{3}$$

$$F = \frac{4}{3}n - 100$$

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

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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".
Re: In a weight-lifting competition, the average (arithmetic mean) of Pier   [#permalink] 04 Jan 2018, 00:13
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