Answer :
To solve this question, we need to find the correct equation that represents the situation of finding the percentage of lemonade in the punch mixture.
We have a recipe ratio that states there are 6 cups of lemonade for every 24 cups of punch. We want to express this as a percentage, which is essentially asking us what percentage of the punch mixture is lemonade.
Here's how we can determine the correct equation:
1. Understanding the Ratio:
The ratio of lemonade to total punch is given as 6 cups of lemonade for every 24 cups of punch. This can be written as a fraction:
[tex]\[
\frac{6}{24}
\][/tex]
This fraction represents the portion of lemonade in the total punch mixture.
2. Convert to Percentage:
To convert this fraction to a percentage, we set up a proportion with [tex]\( x \)[/tex], where [tex]\( x \)[/tex] is the percent of lemonade out of 100.
[tex]\[
\frac{6}{24} = \frac{x}{100}
\][/tex]
3. Cross-Multiply to Solve for [tex]\( x \)[/tex]:
Cross-multiplying to solve for [tex]\( x \)[/tex] gives:
[tex]\[
6 \times 100 = 24 \times x
\][/tex]
[tex]\[
600 = 24x
\][/tex]
Dividing both sides by 24:
[tex]\[
x = \frac{600}{24}
\][/tex]
[tex]\[
x = 25
\][/tex]
So, [tex]\( x = 25 \)[/tex], meaning 25% of the punch is lemonade.
4. Checking Provided Equations:
- OWEN: [tex]\(\frac{24}{6} = \frac{x}{100}\)[/tex] – This is incorrect because it flips the lemonade and punch ratios.
- DIANNA: [tex]\(\frac{6}{30} = \frac{x}{100}\)[/tex] – The numbers don’t match the 24 total cups of punch, so this setup is also incorrect.
- Casey hasn't provided an equation.
Based on this calculation, none of the provided equations seem to match what we derived, but the correct equation to use is:
[tex]\[
\frac{6}{24} = \frac{x}{100}
\][/tex]
It looks like there might have been a misinterpretation in the equations listed. The equation that correctly represents the situation and allows you to find the percentage of lemonade is the one I detailed above.
We have a recipe ratio that states there are 6 cups of lemonade for every 24 cups of punch. We want to express this as a percentage, which is essentially asking us what percentage of the punch mixture is lemonade.
Here's how we can determine the correct equation:
1. Understanding the Ratio:
The ratio of lemonade to total punch is given as 6 cups of lemonade for every 24 cups of punch. This can be written as a fraction:
[tex]\[
\frac{6}{24}
\][/tex]
This fraction represents the portion of lemonade in the total punch mixture.
2. Convert to Percentage:
To convert this fraction to a percentage, we set up a proportion with [tex]\( x \)[/tex], where [tex]\( x \)[/tex] is the percent of lemonade out of 100.
[tex]\[
\frac{6}{24} = \frac{x}{100}
\][/tex]
3. Cross-Multiply to Solve for [tex]\( x \)[/tex]:
Cross-multiplying to solve for [tex]\( x \)[/tex] gives:
[tex]\[
6 \times 100 = 24 \times x
\][/tex]
[tex]\[
600 = 24x
\][/tex]
Dividing both sides by 24:
[tex]\[
x = \frac{600}{24}
\][/tex]
[tex]\[
x = 25
\][/tex]
So, [tex]\( x = 25 \)[/tex], meaning 25% of the punch is lemonade.
4. Checking Provided Equations:
- OWEN: [tex]\(\frac{24}{6} = \frac{x}{100}\)[/tex] – This is incorrect because it flips the lemonade and punch ratios.
- DIANNA: [tex]\(\frac{6}{30} = \frac{x}{100}\)[/tex] – The numbers don’t match the 24 total cups of punch, so this setup is also incorrect.
- Casey hasn't provided an equation.
Based on this calculation, none of the provided equations seem to match what we derived, but the correct equation to use is:
[tex]\[
\frac{6}{24} = \frac{x}{100}
\][/tex]
It looks like there might have been a misinterpretation in the equations listed. The equation that correctly represents the situation and allows you to find the percentage of lemonade is the one I detailed above.
