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Answer :
To find the percent of lemonade in the recipe, we first need to understand the relationship between the amount of lemonade and the total punch mixture.
The recipe specifies 6 cups of lemonade for every 24 cups of punch. To calculate the percentage of lemonade in the punch, we need to compare the amount of lemonade to the total amount of punch.
Here are the steps to solve the problem:
1. Identify the parts and total:
- Lemonade: 6 cups
- Punch: 24 cups
- Total mixture (lemonade + punch): 6 + 24 = 30 cups
2. Set up the proportion for finding the percentage:
- We want to find out what percent 6 cups (lemonade) is of 24 cups (punch).
- The equation that represents this proportion is:
[tex]\(\frac{6}{24} = \frac{x}{100}\)[/tex]
3. Solve the equation:
- To find the percentage [tex]\(x\)[/tex], solve the equation:
Multiply both sides of the equation by 100:
[tex]\[\frac{6}{24} \times 100 = x\][/tex]
- This simplifies to [tex]\(x = 25\)[/tex].
4. Conclusion:
- The percent of lemonade in the recipe is 25%.
Therefore, the correct equation is option A: [tex]\(\frac{6}{24} = \frac{x}{100}\)[/tex].
The recipe specifies 6 cups of lemonade for every 24 cups of punch. To calculate the percentage of lemonade in the punch, we need to compare the amount of lemonade to the total amount of punch.
Here are the steps to solve the problem:
1. Identify the parts and total:
- Lemonade: 6 cups
- Punch: 24 cups
- Total mixture (lemonade + punch): 6 + 24 = 30 cups
2. Set up the proportion for finding the percentage:
- We want to find out what percent 6 cups (lemonade) is of 24 cups (punch).
- The equation that represents this proportion is:
[tex]\(\frac{6}{24} = \frac{x}{100}\)[/tex]
3. Solve the equation:
- To find the percentage [tex]\(x\)[/tex], solve the equation:
Multiply both sides of the equation by 100:
[tex]\[\frac{6}{24} \times 100 = x\][/tex]
- This simplifies to [tex]\(x = 25\)[/tex].
4. Conclusion:
- The percent of lemonade in the recipe is 25%.
Therefore, the correct equation is option A: [tex]\(\frac{6}{24} = \frac{x}{100}\)[/tex].
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