sandy wrote:
Party Cranberry is 3 parts cranberry juice and 1 part seltzer. Fancy Lemonade is 1 part lemon juice and 2 parts seltzer. An amount of Party Cranberry is mixed with an equal amount of Fancy Lemonade.
Quantity A |
Quantity B |
The fraction of the resulting mix that is cranberry juice |
The fraction of the resulting mix that is seltzer |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
GIVEN:
Party Cranberry is 3 parts cranberry juice and 1 part seltzerSo, for every 4 parts of Party Cranberry, there are 3 parts cranberry juice and 1 part seltzer
In other words, Party Cranberry is 3/4 cranberry juice and 1/4 seltzer
Fancy Lemonade is 1 part lemon juice and 2 parts seltzer. So, for every 3 parts of Fancy Lemonade, there are 1 part lemon juice and 2 parts seltzer
In other words, Fancy Lemonade is 1/3 lemon juice and 2/3 seltzer
IMPORTANT CONCEPT: If
EQUAL VOLUMES of 2 solutions are combined, the concentration of the resulting mixture will be the AVERAGE of the 2 solutions.
Example: If 3 liters of a 10% alcohol solution are combined with 3 liters of a 30% alcohol solution, the resulting solution will be 20% alcohol.
Likewise, if 11 liters of 6% alcohol solution are combined with 11 liters of a 7% alcohol solution, the resulting solution will be 6.5% alcohol.
QUANTITY A: The fraction of the resulting mix that is cranberry juice
Party Cranberry is 3/4 cranberry juice, and Fancy Lemonade is 0/4 cranberry juice
So, the fraction of cranberry juice in the resulting mix = (3/4 + 0/4)/2 = 3/8
QUANTITY B: The fraction of the resulting mix that is seltzer
Party Cranberry is 1/4 seltzer, and Fancy Lemonade is 2/3 seltzer
So, the fraction of seltzer in the resulting mix = (1/4 + 2/3)/2 = (3/12 + 8/12)/2 = (11/12)/2 = 11/24
Since 3/8 < 11/24, the answer is B
Cheers,
Brent