Answer :
Sure, let's go through the problem step by step.
1. Understanding the Given Ratio:
- The cleaning spray recipe states that there is [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil.
2. Finding the Rate:
- We need to find out how many cups of vinegar are used per teaspoon of lemon oil.
- To do this, we divide [tex]\(\frac{1}{2}\)[/tex] cup of vinegar by 4 teaspoons:
[tex]\[
\text{Rate} = \frac{\frac{1}{2}}{4} = \frac{1}{8}
\][/tex]
- So, the rate is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per teaspoon of lemon oil.
3. Calculating Vinegar Needed for 2 Teaspoons of Lemon Oil:
- Now that we know the rate is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per teaspoon, we can find out how much vinegar is needed for 2 teaspoons of lemon oil:
[tex]\[
\text{Vinegar needed} = 2 \times \frac{1}{8} = \frac{2}{8} = \frac{1}{4}
\][/tex]
- Therefore, [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed for 2 teaspoons of lemon oil.
4. Verification with Given Adjusted Ratio:
- It's noted that the actual given ratio for 2 teaspoons of lemon oil and vinegar is [tex]\(\frac{1}{4}\)[/tex] cup of vinegar.
- This matches the calculated amount, confirming the solution is consistent.
5. Summary:
- The rate of vinegar per teaspoon of lemon oil is [tex]\(\frac{1}{8}\)[/tex] cup.
- For 2 teaspoons of lemon oil, [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed, which is consistent with the given ratio of [tex]\(\frac{1}{4}\)[/tex] cup for 2 teaspoons.
Everything checks out correctly!
1. Understanding the Given Ratio:
- The cleaning spray recipe states that there is [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil.
2. Finding the Rate:
- We need to find out how many cups of vinegar are used per teaspoon of lemon oil.
- To do this, we divide [tex]\(\frac{1}{2}\)[/tex] cup of vinegar by 4 teaspoons:
[tex]\[
\text{Rate} = \frac{\frac{1}{2}}{4} = \frac{1}{8}
\][/tex]
- So, the rate is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per teaspoon of lemon oil.
3. Calculating Vinegar Needed for 2 Teaspoons of Lemon Oil:
- Now that we know the rate is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per teaspoon, we can find out how much vinegar is needed for 2 teaspoons of lemon oil:
[tex]\[
\text{Vinegar needed} = 2 \times \frac{1}{8} = \frac{2}{8} = \frac{1}{4}
\][/tex]
- Therefore, [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed for 2 teaspoons of lemon oil.
4. Verification with Given Adjusted Ratio:
- It's noted that the actual given ratio for 2 teaspoons of lemon oil and vinegar is [tex]\(\frac{1}{4}\)[/tex] cup of vinegar.
- This matches the calculated amount, confirming the solution is consistent.
5. Summary:
- The rate of vinegar per teaspoon of lemon oil is [tex]\(\frac{1}{8}\)[/tex] cup.
- For 2 teaspoons of lemon oil, [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed, which is consistent with the given ratio of [tex]\(\frac{1}{4}\)[/tex] cup for 2 teaspoons.
Everything checks out correctly!
