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07 Sep 2021, 03:29
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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) \(\frac{(100b - bq + qr)}{(10,000b - 100bq)}\)
(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) \(\frac{(100b - bq + qr)}{(10,000b - 100bq)}\)
09 Oct 2021, 01:59
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This might turn into a disaster without formatting. Apologies. On my phone.
Let the total Quantity of Tokens = X
“q percent of player A’s TOKENS are red”
(q%) (X) = number of red tokens
This means that (100 - q)% of the total X tokens must be blue
(100 - q)% (X) = number of blue tokens
“p percent of player A’s POINTS are from blue tokens”
Each blue token gives B points
Each red token gives R points
Total Points = (# of red tokens) (R points) + (# of blue tokens) (B points)
Total points = (q%) (X) (R) + (100 - q)% (X) (B)
Blue Points = (100 - q)% (X) (B)
P% * (Total Points) = Blue Points
Or
P% = (Blue Points) / (Total Points)
P% = (100 - q)% (X) (B) / [ (100 - q)% (X) (B) + (q)% (X) (R) ]
——the X = Total number of Tokens cancels out in the NUM and DEN as it is part of each term ——
P% =
(100 - q) (B) / 100
________________
[(100 - q) (B) /100 ] + [ (q) (R) / 100]
——as 100 is in the DEN of each term we can Multiply the entire fraction by *(100/100) to remove all of the 100s in the DEN’s——
P% =
(B) (100 - q)
_________________
(B) (100 - q) + (R) (q)
P% =
100B - Bq
___________
100B - Bq + Rq
Now to solve in terms of “p”, we need to multiply each side of the equation to get rid of the percentage %
P =
(10,000)(B) - (100)(B)(q)
_____________________
(100)(B) - (B)(q) + (R)(q)
Which matches answer B
Correct answer (B)
Note: this is a spin on the newspaper percentage question in the official guide
Posted from my mobile device
Let the total Quantity of Tokens = X
“q percent of player A’s TOKENS are red”
(q%) (X) = number of red tokens
This means that (100 - q)% of the total X tokens must be blue
(100 - q)% (X) = number of blue tokens
“p percent of player A’s POINTS are from blue tokens”
Each blue token gives B points
Each red token gives R points
Total Points = (# of red tokens) (R points) + (# of blue tokens) (B points)
Total points = (q%) (X) (R) + (100 - q)% (X) (B)
Blue Points = (100 - q)% (X) (B)
P% * (Total Points) = Blue Points
Or
P% = (Blue Points) / (Total Points)
P% = (100 - q)% (X) (B) / [ (100 - q)% (X) (B) + (q)% (X) (R) ]
——the X = Total number of Tokens cancels out in the NUM and DEN as it is part of each term ——
P% =
(100 - q) (B) / 100
________________
[(100 - q) (B) /100 ] + [ (q) (R) / 100]
——as 100 is in the DEN of each term we can Multiply the entire fraction by *(100/100) to remove all of the 100s in the DEN’s——
P% =
(B) (100 - q)
_________________
(B) (100 - q) + (R) (q)
P% =
100B - Bq
___________
100B - Bq + Rq
Now to solve in terms of “p”, we need to multiply each side of the equation to get rid of the percentage %
P =
(10,000)(B) - (100)(B)(q)
_____________________
(100)(B) - (B)(q) + (R)(q)
Which matches answer B
Correct answer (B)
Note: this is a spin on the newspaper percentage question in the official guide
Posted from my mobile device
25 Jan 2025, 12:29
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Let's assume b = 2, r = 4
Assuming, no. of blue tokens collected (x) = 3, and no. of red tokens collected (y) = 1
Total points = 2*3 + 4*1 = 10
p% of points are from blue tokens => we got 6 points from blue tokens => p = 60
q% of tokens are red => we have 1 red token of total 4 tokens = 1/4 = 25% => q = 25
We have values of b, r and q; substituting them in answer choices we should get 60. Option B gives 60 when b = 2, r = 4, and q = 25
Answer B.
Assuming, no. of blue tokens collected (x) = 3, and no. of red tokens collected (y) = 1
Total points = 2*3 + 4*1 = 10
p% of points are from blue tokens => we got 6 points from blue tokens => p = 60
q% of tokens are red => we have 1 red token of total 4 tokens = 1/4 = 25% => q = 25
We have values of b, r and q; substituting them in answer choices we should get 60. Option B gives 60 when b = 2, r = 4, and q = 25
Answer B.
