Answer :
To solve this problem, we need to figure out two things:
1. The number of cups of vinegar needed for 2 teaspoons of lemon oil.
2. The rate in cups of vinegar per teaspoon of lemon oil.
Here's how you solve it step-by-step:
1. Understand the initial proportion:
The cleaning spray uses [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil. This is our starting proportion.
2. Find the rate of vinegar per teaspoon of lemon oil:
To find out how much vinegar is used per one teaspoon of lemon oil, we divide the number of cups of vinegar by the number of teaspoons of lemon oil:
[tex]\[
\text{Rate of vinegar per tsp of lemon oil} = \frac{1}{2} \div 4 = 0.125
\][/tex]
So, the rate is 0.125 cups of vinegar per teaspoon of lemon oil.
3. Calculate vinegar needed for 2 teaspoons of lemon oil:
Now that we know the rate (0.125 cups per teaspoon), we can find out how much vinegar is needed for 2 teaspoons by multiplying the rate by 2:
[tex]\[
\text{Vinegar for 2 tsp of lemon oil} = 0.125 \times 2 = 0.25
\][/tex]
Therefore, 0.25 cups of vinegar are needed for 2 teaspoons of lemon oil.
To summarize:
- The rate is 0.125 cups of vinegar per teaspoon of lemon oil.
- The amount of vinegar needed for 2 teaspoons of lemon oil is 0.25 cups.
1. The number of cups of vinegar needed for 2 teaspoons of lemon oil.
2. The rate in cups of vinegar per teaspoon of lemon oil.
Here's how you solve it step-by-step:
1. Understand the initial proportion:
The cleaning spray uses [tex]\(\frac{1}{2}\)[/tex] cup of vinegar for every 4 teaspoons of lemon oil. This is our starting proportion.
2. Find the rate of vinegar per teaspoon of lemon oil:
To find out how much vinegar is used per one teaspoon of lemon oil, we divide the number of cups of vinegar by the number of teaspoons of lemon oil:
[tex]\[
\text{Rate of vinegar per tsp of lemon oil} = \frac{1}{2} \div 4 = 0.125
\][/tex]
So, the rate is 0.125 cups of vinegar per teaspoon of lemon oil.
3. Calculate vinegar needed for 2 teaspoons of lemon oil:
Now that we know the rate (0.125 cups per teaspoon), we can find out how much vinegar is needed for 2 teaspoons by multiplying the rate by 2:
[tex]\[
\text{Vinegar for 2 tsp of lemon oil} = 0.125 \times 2 = 0.25
\][/tex]
Therefore, 0.25 cups of vinegar are needed for 2 teaspoons of lemon oil.
To summarize:
- The rate is 0.125 cups of vinegar per teaspoon of lemon oil.
- The amount of vinegar needed for 2 teaspoons of lemon oil is 0.25 cups.
