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Senior RC Moderator V
Joined: 02 Nov 2016
Posts: 3448
GPA: 3.39
A certain game requires players to collect both blue tokens, which are  [#permalink]

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7 00:00

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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Math Expert V
Joined: 02 Aug 2009
Posts: 7756
Re: A certain game requires players to collect both blue tokens, which are  [#permalink]

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2
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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Director  V
Joined: 27 May 2012
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Re: A certain game requires players to collect both blue tokens, which are  [#permalink]

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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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- Stne
Math Expert V
Joined: 02 Aug 2009
Posts: 7756
Re: A certain game requires players to collect both blue tokens, which are  [#permalink]

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1
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
_________________ Re: A certain game requires players to collect both blue tokens, which are   [#permalink] 08 Apr 2019, 21:08
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