Answer :
To solve this problem, we need to determine the relationship between the ounces of water, [tex]\( w \)[/tex], and the tablespoons of lemon juice, [tex]\( j \)[/tex].
We know from the problem statement that for every 8 ounces of water, Sia uses [tex]\(\frac{1}{2}\)[/tex] tablespoon of lemon juice. We want to create an equation that shows this relationship for any amount of water, [tex]\( w \)[/tex], and lemon juice, [tex]\( j \)[/tex].
1. Understand the ratio given:
- The ratio of water to lemon juice is 8 ounces to [tex]\(\frac{1}{2}\)[/tex] tablespoon.
2. Convert this into a form usable for all [tex]\( j \)[/tex]:
- Let's find out how many ounces of water would go with 1 tablespoon of lemon juice.
- Since [tex]\(\frac{1}{2}\)[/tex] tablespoon corresponds to 8 ounces, we find the amount for 1 full tablespoon of lemon juice by doubling the amount of water.
3. Calculate the ratio:
- Double the amount of water for 1 tablespoon of lemon juice: [tex]\( 8 \text{ oz} \times 2 = 16 \text{ oz} \)[/tex].
- This means for every 1 tablespoon of lemon juice, there are 16 ounces of water.
4. Write the equation:
- The relationship is: [tex]\( w = 16j \)[/tex]
Thus, the equation that shows the relationship between the ounces of water, [tex]\( w \)[/tex], and the tablespoons of lemon juice, [tex]\( j \)[/tex], is:
[tex]\[ w = 16j \][/tex]
So, the correct answer is B [tex]\( w = 16j \)[/tex].
We know from the problem statement that for every 8 ounces of water, Sia uses [tex]\(\frac{1}{2}\)[/tex] tablespoon of lemon juice. We want to create an equation that shows this relationship for any amount of water, [tex]\( w \)[/tex], and lemon juice, [tex]\( j \)[/tex].
1. Understand the ratio given:
- The ratio of water to lemon juice is 8 ounces to [tex]\(\frac{1}{2}\)[/tex] tablespoon.
2. Convert this into a form usable for all [tex]\( j \)[/tex]:
- Let's find out how many ounces of water would go with 1 tablespoon of lemon juice.
- Since [tex]\(\frac{1}{2}\)[/tex] tablespoon corresponds to 8 ounces, we find the amount for 1 full tablespoon of lemon juice by doubling the amount of water.
3. Calculate the ratio:
- Double the amount of water for 1 tablespoon of lemon juice: [tex]\( 8 \text{ oz} \times 2 = 16 \text{ oz} \)[/tex].
- This means for every 1 tablespoon of lemon juice, there are 16 ounces of water.
4. Write the equation:
- The relationship is: [tex]\( w = 16j \)[/tex]
Thus, the equation that shows the relationship between the ounces of water, [tex]\( w \)[/tex], and the tablespoons of lemon juice, [tex]\( j \)[/tex], is:
[tex]\[ w = 16j \][/tex]
So, the correct answer is B [tex]\( w = 16j \)[/tex].
