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Answer :
Sure, let's solve this step-by-step.
The problem states that the cleaning spray contains [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil.
We want to find out how many cups of vinegar are needed for 2 teaspoons of lemon oil.
Here's how we can solve it:
1. Identify the known ratio:
The ratio of vinegar to lemon oil is [tex]\(\frac{1}{2}\)[/tex] cup of vinegar per 4 teaspoons of lemon oil.
2. Find the amount of vinegar per teaspoon of lemon oil:
To find out how much vinegar is used per teaspoon of lemon oil, divide [tex]\(\frac{1}{2}\)[/tex] cup by 4 teaspoons:
[tex]\[
\text{Vinegar per teaspoon} = \frac{1}{2} \div 4 = \frac{1}{8} \text{ cup of vinegar per teaspoon of lemon oil}
\][/tex]
3. Calculate the vinegar for 2 teaspoons of lemon oil:
Multiply the amount of vinegar per teaspoon by the number of teaspoons:
[tex]\[
\text{Vinegar for 2 teaspoons} = \frac{1}{8} \times 2 = \frac{1}{4} \text{ cup of vinegar}
\][/tex]
Therefore, [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed for 2 teaspoons of lemon oil.
The problem states that the cleaning spray contains [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil.
We want to find out how many cups of vinegar are needed for 2 teaspoons of lemon oil.
Here's how we can solve it:
1. Identify the known ratio:
The ratio of vinegar to lemon oil is [tex]\(\frac{1}{2}\)[/tex] cup of vinegar per 4 teaspoons of lemon oil.
2. Find the amount of vinegar per teaspoon of lemon oil:
To find out how much vinegar is used per teaspoon of lemon oil, divide [tex]\(\frac{1}{2}\)[/tex] cup by 4 teaspoons:
[tex]\[
\text{Vinegar per teaspoon} = \frac{1}{2} \div 4 = \frac{1}{8} \text{ cup of vinegar per teaspoon of lemon oil}
\][/tex]
3. Calculate the vinegar for 2 teaspoons of lemon oil:
Multiply the amount of vinegar per teaspoon by the number of teaspoons:
[tex]\[
\text{Vinegar for 2 teaspoons} = \frac{1}{8} \times 2 = \frac{1}{4} \text{ cup of vinegar}
\][/tex]
Therefore, [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed for 2 teaspoons of lemon oil.
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