Answer :
Sure! Let's work through the solution step-by-step:
1. Understanding the ratio: We are given that the cleaning spray contains [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil. This gives us a rate, or ratio, of vinegar to lemon oil.
2. Calculate the rate of vinegar per teaspoon of lemon oil:
Since [tex]\(\frac{1}{2}\)[/tex] cup of vinegar is used for 4 teaspoons of lemon oil, we can find the amount of vinegar needed for one teaspoon of lemon oil by dividing the vinegar amount by 4:
[tex]\[
\text{Rate of vinegar per teaspoon} = \frac{\frac{1}{2} \text{ cup of vinegar}}{4 \text{ teaspoons of lemon oil}} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \text{ cup per teaspoon}
\][/tex]
Therefore, the rate is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per teaspoon of lemon oil.
3. Calculate the amount of vinegar needed for 2 teaspoons of lemon oil:
Now, we need to find out how much vinegar is needed for 2 teaspoons of lemon oil. Using the rate from above, you will multiply the rate by 2:
[tex]\[
\text{Vinegar for 2 teaspoons} = 2 \text{ teaspoons} \times \frac{1}{8} \text{ cup per teaspoon} = \frac{2}{8} \text{ cup} = \frac{1}{4} \text{ cup}
\][/tex]
So, for 2 teaspoons of lemon oil, [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed, and the rate is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per teaspoon of lemon oil.
1. Understanding the ratio: We are given that the cleaning spray contains [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil. This gives us a rate, or ratio, of vinegar to lemon oil.
2. Calculate the rate of vinegar per teaspoon of lemon oil:
Since [tex]\(\frac{1}{2}\)[/tex] cup of vinegar is used for 4 teaspoons of lemon oil, we can find the amount of vinegar needed for one teaspoon of lemon oil by dividing the vinegar amount by 4:
[tex]\[
\text{Rate of vinegar per teaspoon} = \frac{\frac{1}{2} \text{ cup of vinegar}}{4 \text{ teaspoons of lemon oil}} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \text{ cup per teaspoon}
\][/tex]
Therefore, the rate is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per teaspoon of lemon oil.
3. Calculate the amount of vinegar needed for 2 teaspoons of lemon oil:
Now, we need to find out how much vinegar is needed for 2 teaspoons of lemon oil. Using the rate from above, you will multiply the rate by 2:
[tex]\[
\text{Vinegar for 2 teaspoons} = 2 \text{ teaspoons} \times \frac{1}{8} \text{ cup per teaspoon} = \frac{2}{8} \text{ cup} = \frac{1}{4} \text{ cup}
\][/tex]
So, for 2 teaspoons of lemon oil, [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed, and the rate is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per teaspoon of lemon oil.
