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An incredible punch is composed of buttermilk...

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by swerve » Thu Feb 22, 2018 4:35 am
An incredible punch is composed of buttermilk, orange juice, and brandy. How many pints of orange juice are required to make 7 1/2 gallons of punch containing twice as much buttermilk as orange juice and three times as much orange juice as brandy? (1 gallon = 8 pints).

A. 16
B. 18
C. 20
D. 22
E. 24

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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by DavidG@VeritasPrep » Thu Feb 22, 2018 8:12 am
swerve wrote:An incredible punch is composed of buttermilk, orange juice, and brandy. How many pints of orange juice are required to make 7 1/2 gallons of punch containing twice as much buttermilk as orange juice and three times as much orange juice as brandy? (1 gallon = 8 pints).

A. 16
B. 18
C. 20
D. 22
E. 24

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
Call the Brandy amount 'B.' If there's three times as much orange juice, there'd be '3B' gallons. And if there were twice as much buttermilk as orange juice, there'd be 6B gallons of bulltermilk. To summarize:

Brandy: B
Orange Juice: 3B
Buttermilk: 6B
Total: 10B

We know this should sum to 7.5 gallons of punch, so 10B = 7.5 --> B = .75 = 3/4
Total gallons of orange juice: 3B = 3(3/4) = 9/4
9/4 gallons = 9/4 * 8 = 18 pints. The answer is B
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by Jeff@TargetTestPrep » Mon Feb 26, 2018 10:02 am
swerve wrote:An incredible punch is composed of buttermilk, orange juice, and brandy. How many pints of orange juice are required to make 7 1/2 gallons of punch containing twice as much buttermilk as orange juice and three times as much orange juice as brandy? (1 gallon = 8 pints).

A. 16
B. 18
C. 20
D. 22
E. 24
We need to make 7½ gallons of punch, or 7½ x 8 = 60 pints of punch. We can let x = the number of pints of brandy needed; thus, 3x = the number of pints of orange juice and 2(3x) = 6x = the number of pints of buttermilk. We can create the following equation:

6x + 3x + x = 60

10x = 60

x = 6

Thus, we need 3(6) = 18 pints of orange juice.

Answer: B

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