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Answer :
Sure! Let's solve this step-by-step:
1. Understand the Given Ratio:
- The cleaning spray recipe mentioned uses [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil. This is our starting ratio.
2. Find the Rate of Vinegar per Teaspoon of Lemon Oil:
- To find out how many cups of vinegar are needed per teaspoon of lemon oil, we need to convert the recipe into that unit. We divide the amount of vinegar by the number of teaspoons of lemon oil.
- So, [tex]\(\frac{1}{2}\)[/tex] cup of vinegar divided by 4 teaspoons of lemon oil is calculated as:
[tex]\[
\frac{\frac{1}{2}}{4} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \, \text{cup of vinegar per teaspoon of lemon oil}
\][/tex]
- So, the rate is [tex]\(0.125\)[/tex] cups of vinegar per teaspoon.
3. Calculate Vinegar Needed for 2 Teaspoons of Lemon Oil:
- Now, we want to know how many cups of vinegar are needed for 2 teaspoons of lemon oil.
- Using the rate we just found, we multiply:
[tex]\[
\frac{1}{8} \, \text{cup of vinegar per teaspoon} \times 2 \, \text{teaspoons} = \frac{2}{8} = \frac{1}{4} \, \text{cup of vinegar}
\][/tex]
- This means you need [tex]\(0.25\)[/tex] cups of vinegar for 2 teaspoons of lemon oil.
In summary, the rate of vinegar per teaspoon of lemon oil is [tex]\(0.125\)[/tex] cups, and for 2 teaspoons of lemon oil, you need [tex]\(0.25\)[/tex] cups of vinegar.
1. Understand the Given Ratio:
- The cleaning spray recipe mentioned uses [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil. This is our starting ratio.
2. Find the Rate of Vinegar per Teaspoon of Lemon Oil:
- To find out how many cups of vinegar are needed per teaspoon of lemon oil, we need to convert the recipe into that unit. We divide the amount of vinegar by the number of teaspoons of lemon oil.
- So, [tex]\(\frac{1}{2}\)[/tex] cup of vinegar divided by 4 teaspoons of lemon oil is calculated as:
[tex]\[
\frac{\frac{1}{2}}{4} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \, \text{cup of vinegar per teaspoon of lemon oil}
\][/tex]
- So, the rate is [tex]\(0.125\)[/tex] cups of vinegar per teaspoon.
3. Calculate Vinegar Needed for 2 Teaspoons of Lemon Oil:
- Now, we want to know how many cups of vinegar are needed for 2 teaspoons of lemon oil.
- Using the rate we just found, we multiply:
[tex]\[
\frac{1}{8} \, \text{cup of vinegar per teaspoon} \times 2 \, \text{teaspoons} = \frac{2}{8} = \frac{1}{4} \, \text{cup of vinegar}
\][/tex]
- This means you need [tex]\(0.25\)[/tex] cups of vinegar for 2 teaspoons of lemon oil.
In summary, the rate of vinegar per teaspoon of lemon oil is [tex]\(0.125\)[/tex] cups, and for 2 teaspoons of lemon oil, you need [tex]\(0.25\)[/tex] cups of vinegar.
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