Answer :
Let's look at the given options to determine which one contains 5 oz of pure alcohol. We'll calculate the total amount of alcohol for each option using the alcohol by volume (ABV) contained in spirits, beer, and wine.
Alcohol by Volume (ABV):
- Proof is twice the ABV percentage.
- Spirits (100 proof is 50% ABV, 80 proof is 40% ABV).
- Beer typically has 5% ABV.
- Wine typically has 12% ABV.
### Option 1:
1 oz of 100 proof spirits, 12 oz of beer, and 5 oz of wine.
- Spirits: [tex]\( 1 \, \text{oz} \times 50\% = 0.5 \, \text{oz of pure alcohol} \)[/tex]
- Beer: [tex]\( 12 \, \text{oz} \times 5\% = 0.6 \, \text{oz of pure alcohol} \)[/tex]
- Wine: [tex]\( 5 \, \text{oz} \times 12\% = 0.6 \, \text{oz of pure alcohol} \)[/tex]
Total alcohol content: [tex]\( 0.5 + 0.6 + 0.6 = 1.7 \, \text{oz of pure alcohol} \)[/tex]
### Option 2:
2 oz of 80 proof spirits, 16 oz of beer, and 6 oz of wine.
- Spirits: [tex]\( 2 \, \text{oz} \times 40\% = 0.8 \, \text{oz of pure alcohol} \)[/tex]
- Beer: [tex]\( 16 \, \text{oz} \times 5\% = 0.8 \, \text{oz of pure alcohol} \)[/tex]
- Wine: [tex]\( 6 \, \text{oz} \times 12\% = 0.72 \, \text{oz of pure alcohol} \)[/tex]
Total alcohol content: [tex]\( 0.8 + 0.8 + 0.72 = 2.32 \, \text{oz of pure alcohol} \)[/tex]
### Option 3:
1 oz of 80 proof spirits, 12 oz of beer, and 7 oz of wine.
- Spirits: [tex]\( 1 \, \text{oz} \times 40\% = 0.4 \, \text{oz of pure alcohol} \)[/tex]
- Beer: [tex]\( 12 \, \text{oz} \times 5\% = 0.6 \, \text{oz of pure alcohol} \)[/tex]
- Wine: [tex]\( 7 \, \text{oz} \times 12\% = 0.84 \, \text{oz of pure alcohol} \)[/tex]
Total alcohol content: [tex]\( 0.4 + 0.6 + 0.84 = 1.84 \, \text{oz of pure alcohol} \)[/tex]
### Analysis:
We need to identify which option contains the amount of pure alcohol closest to 5 oz.
- Option 1: 1.7 oz of pure alcohol
- Option 2: 2.32 oz of pure alcohol
- Option 3: 1.84 oz of pure alcohol
None of the options provide exactly 5 oz of pure alcohol, however, by evaluating the results, we see that none of the options come close to the required 5 oz mark. If any detail were incorrect with the question parameters or desired results, you may consider re-evaluating the question for any inconsistencies or differing expectations.
Alcohol by Volume (ABV):
- Proof is twice the ABV percentage.
- Spirits (100 proof is 50% ABV, 80 proof is 40% ABV).
- Beer typically has 5% ABV.
- Wine typically has 12% ABV.
### Option 1:
1 oz of 100 proof spirits, 12 oz of beer, and 5 oz of wine.
- Spirits: [tex]\( 1 \, \text{oz} \times 50\% = 0.5 \, \text{oz of pure alcohol} \)[/tex]
- Beer: [tex]\( 12 \, \text{oz} \times 5\% = 0.6 \, \text{oz of pure alcohol} \)[/tex]
- Wine: [tex]\( 5 \, \text{oz} \times 12\% = 0.6 \, \text{oz of pure alcohol} \)[/tex]
Total alcohol content: [tex]\( 0.5 + 0.6 + 0.6 = 1.7 \, \text{oz of pure alcohol} \)[/tex]
### Option 2:
2 oz of 80 proof spirits, 16 oz of beer, and 6 oz of wine.
- Spirits: [tex]\( 2 \, \text{oz} \times 40\% = 0.8 \, \text{oz of pure alcohol} \)[/tex]
- Beer: [tex]\( 16 \, \text{oz} \times 5\% = 0.8 \, \text{oz of pure alcohol} \)[/tex]
- Wine: [tex]\( 6 \, \text{oz} \times 12\% = 0.72 \, \text{oz of pure alcohol} \)[/tex]
Total alcohol content: [tex]\( 0.8 + 0.8 + 0.72 = 2.32 \, \text{oz of pure alcohol} \)[/tex]
### Option 3:
1 oz of 80 proof spirits, 12 oz of beer, and 7 oz of wine.
- Spirits: [tex]\( 1 \, \text{oz} \times 40\% = 0.4 \, \text{oz of pure alcohol} \)[/tex]
- Beer: [tex]\( 12 \, \text{oz} \times 5\% = 0.6 \, \text{oz of pure alcohol} \)[/tex]
- Wine: [tex]\( 7 \, \text{oz} \times 12\% = 0.84 \, \text{oz of pure alcohol} \)[/tex]
Total alcohol content: [tex]\( 0.4 + 0.6 + 0.84 = 1.84 \, \text{oz of pure alcohol} \)[/tex]
### Analysis:
We need to identify which option contains the amount of pure alcohol closest to 5 oz.
- Option 1: 1.7 oz of pure alcohol
- Option 2: 2.32 oz of pure alcohol
- Option 3: 1.84 oz of pure alcohol
None of the options provide exactly 5 oz of pure alcohol, however, by evaluating the results, we see that none of the options come close to the required 5 oz mark. If any detail were incorrect with the question parameters or desired results, you may consider re-evaluating the question for any inconsistencies or differing expectations.
