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A certain game requires players to collect both blue tokens, which are

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A certain game requires players to collect both blue tokens, which are  [#permalink]

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New post 07 Feb 2019, 12:17
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Difficulty:

  75% (hard)

Question Stats:

38% (03:20) correct 62% (03:02) wrong based on 26 sessions

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A certain game requires players to collect both blue tokens, which are worth b points each, and red tokens, which are worth r points each. If p percent of player A's points are from blue tokens and q percent of player A's token are red, which of the following is an expression for the value of p, in terms of b, r, and q?

A) \(\frac{100bq}{(bq + 100r - qr)}\)

B) \(\frac{(10,000b - 100bq)}{(100b - bq + qr )}\)

C) \(\frac{(bq + 100r - qr)}{100 bq}\)

D) \(\frac{(100b - bq)}{(100r - 100bq - qr)}\)

E) \(\frac{(100b - bq + qr)}{(10,000b - 100bq)}\)

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Re: A certain game requires players to collect both blue tokens, which are  [#permalink]

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New post 07 Feb 2019, 20:19
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SajjadAhmad wrote:
A certain game requires players to collect both blue tokens, which are worth b points each, and red tokens, which are worth r points each. If p percent of player A's points are from blue tokens and q percent of player A's token are red, which of the following is an expression for the value of p, in terms of b, r, and q?

A) \(\frac{100bq}{(bq + 100r - qr)}\)

B) \(\frac{(10,000b - 100bq)}{(100b - bq + qr )}\)

C) \(\frac{(bq + 100r - qr)}{100 bq}\)

D) \(\frac{(100b - bq)}{(100r - 100bq - qr)}\)

E) \(\frac{(100b - bq + qr)}{(10,000b - 100bq)}\)


Let the total number be 100, as this is a percentage question..

Now p+q=100 or p=100-q..
Value of blue = pb, and value of red = qr
Percentage of value of b = \(100*\frac{pb}{pb+qr}\)
Substitute p =100-q, so Percentage of value of b =p= \(100*\frac{(100-q)b}{(100-q)b+qr}\)= \(\frac{(10,000b - 100bq)}{(100b - bq + qr )}\)

B
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Re: A certain game requires players to collect both blue tokens, which are  [#permalink]

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New post 08 Apr 2019, 20:51
chetan2u wrote:
SajjadAhmad wrote:
A certain game requires players to collect both blue tokens, which are worth b points each, and red tokens, which are worth r points each. If p percent of player A's points are from blue tokens and q percent of player A's token are red, which of the following is an expression for the value of p, in terms of b, r, and q?

A) \(\frac{100bq}{(bq + 100r - qr)}\)

B) \(\frac{(10,000b - 100bq)}{(100b - bq + qr )}\)

C) \(\frac{(bq + 100r - qr)}{100 bq}\)

D) \(\frac{(100b - bq)}{(100r - 100bq - qr)}\)

E) \(\frac{(100b - bq + qr)}{(10,000b - 100bq)}\)


Let the total number be 100, as this is a percentage question..

Now p+q=100 or p=100-q..
Value of blue = pb, and value of red = qr
Percentage of value of b = \(100*\frac{pb}{pb+qr}\)
Substitute p =100-q, so Percentage of value of b =p= \(100*\frac{(100-q)b}{(100-q)b+qr}\)= \(\frac{(10,000b - 100bq)}{(100b - bq + qr )}\)

B



Hi chetan2u,
Can you elaborate how the value of blue is pb and value of red is qr.
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Re: A certain game requires players to collect both blue tokens, which are  [#permalink]

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New post 08 Apr 2019, 21:08
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stne wrote:
chetan2u wrote:
SajjadAhmad wrote:
A certain game requires players to collect both blue tokens, which are worth b points each, and red tokens, which are worth r points each. If p percent of player A's points are from blue tokens and q percent of player A's token are red, which of the following is an expression for the value of p, in terms of b, r, and q?

A) \(\frac{100bq}{(bq + 100r - qr)}\)

B) \(\frac{(10,000b - 100bq)}{(100b - bq + qr )}\)

C) \(\frac{(bq + 100r - qr)}{100 bq}\)

D) \(\frac{(100b - bq)}{(100r - 100bq - qr)}\)

E) \(\frac{(100b - bq + qr)}{(10,000b - 100bq)}\)


Let the total number be 100, as this is a percentage question..

Now p+q=100 or p=100-q..
Value of blue = pb, and value of red = qr
Percentage of value of b = \(100*\frac{pb}{pb+qr}\)
Substitute p =100-q, so Percentage of value of b =p= \(100*\frac{(100-q)b}{(100-q)b+qr}\)= \(\frac{(10,000b - 100bq)}{(100b - bq + qr )}\)

B


Hi chetan2u,
Can you elaborate how the value of blue is pb and value of red is qr.


Hi..
I have taken the total to be 100.. so p percent of 100 is (p/100)*100=p.
Thus we have p blue tokens and each blue tokens worth B points. Total = number of tokens *points per token = p*b

Similarly for other
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Re: A certain game requires players to collect both blue tokens, which are   [#permalink] 08 Apr 2019, 21:08
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