Answer :
Certainly! Let's work through the problem step by step.
Sia uses [tex]\(\frac{1}{2}\)[/tex] tablespoon (tbsp) of lemon juice for every 8 ounces (oz) of water. We need to find the equation that shows the relationship between the ounces of water ([tex]\( w \)[/tex]) and tablespoons of lemon juice ([tex]\( j \)[/tex]).
1. Understanding the Ratio:
- [tex]\( \frac{1}{2} \)[/tex] tbsp of lemon juice is used for 8 oz of water.
- This means for each ounce of water, the amount of lemon juice used is [tex]\(\frac{\frac{1}{2}}{8}\)[/tex].
2. Calculate the Lemon Juice per Ounce of Water:
- [tex]\(\frac{\frac{1}{2}}{8} = \frac{1}{2} \times \frac{1}{8} = \frac{1}{16}\)[/tex] tbsp of lemon juice per ounce of water.
3. Express the Relationship in an Equation:
- Let [tex]\( w \)[/tex] represent the ounces of water.
- Let [tex]\( j \)[/tex] represent the tablespoons of lemon juice.
- From the ratio, we have: [tex]\( j = \frac{1}{16} w \)[/tex].
4. Finding the Correct Equation:
- We need to check which of the given options matches [tex]\( j = \frac{1}{16} w \)[/tex].
Let's look at each option:
- Option A: [tex]\( w = 4 j \)[/tex]:
- This suggests [tex]\( j = \frac{w}{4} \)[/tex]. This does not match [tex]\( j = \frac{1}{16} w \)[/tex].
- Option B: [tex]\( w = 16 j \)[/tex]:
- This suggests [tex]\( j = \frac{w}{16} \)[/tex]. This does match with [tex]\( j = \frac{1}{16} w \)[/tex].
- Option C: [tex]\( j = 4 w \)[/tex]:
- This suggests [tex]\( j \)[/tex] increases at a much faster rate compared to how water is being added. This does not match [tex]\( j = \frac{1}{16} w \)[/tex].
- Option D: [tex]\( j = 16 w \)[/tex]:
- This suggests [tex]\( j \)[/tex] increases 16 times the rate of [tex]\( w \)[/tex] which also does not match [tex]\( j = \frac{1}{16} w \)[/tex].
By comparing our derived equation [tex]\( j = \frac{1}{16} w \)[/tex] with the options given, the correct option that accurately represents the relationship between [tex]\( w \)[/tex] and [tex]\( j \)[/tex] is:
B. [tex]\( w = 16 j \)[/tex]
Sia uses [tex]\(\frac{1}{2}\)[/tex] tablespoon (tbsp) of lemon juice for every 8 ounces (oz) of water. We need to find the equation that shows the relationship between the ounces of water ([tex]\( w \)[/tex]) and tablespoons of lemon juice ([tex]\( j \)[/tex]).
1. Understanding the Ratio:
- [tex]\( \frac{1}{2} \)[/tex] tbsp of lemon juice is used for 8 oz of water.
- This means for each ounce of water, the amount of lemon juice used is [tex]\(\frac{\frac{1}{2}}{8}\)[/tex].
2. Calculate the Lemon Juice per Ounce of Water:
- [tex]\(\frac{\frac{1}{2}}{8} = \frac{1}{2} \times \frac{1}{8} = \frac{1}{16}\)[/tex] tbsp of lemon juice per ounce of water.
3. Express the Relationship in an Equation:
- Let [tex]\( w \)[/tex] represent the ounces of water.
- Let [tex]\( j \)[/tex] represent the tablespoons of lemon juice.
- From the ratio, we have: [tex]\( j = \frac{1}{16} w \)[/tex].
4. Finding the Correct Equation:
- We need to check which of the given options matches [tex]\( j = \frac{1}{16} w \)[/tex].
Let's look at each option:
- Option A: [tex]\( w = 4 j \)[/tex]:
- This suggests [tex]\( j = \frac{w}{4} \)[/tex]. This does not match [tex]\( j = \frac{1}{16} w \)[/tex].
- Option B: [tex]\( w = 16 j \)[/tex]:
- This suggests [tex]\( j = \frac{w}{16} \)[/tex]. This does match with [tex]\( j = \frac{1}{16} w \)[/tex].
- Option C: [tex]\( j = 4 w \)[/tex]:
- This suggests [tex]\( j \)[/tex] increases at a much faster rate compared to how water is being added. This does not match [tex]\( j = \frac{1}{16} w \)[/tex].
- Option D: [tex]\( j = 16 w \)[/tex]:
- This suggests [tex]\( j \)[/tex] increases 16 times the rate of [tex]\( w \)[/tex] which also does not match [tex]\( j = \frac{1}{16} w \)[/tex].
By comparing our derived equation [tex]\( j = \frac{1}{16} w \)[/tex] with the options given, the correct option that accurately represents the relationship between [tex]\( w \)[/tex] and [tex]\( j \)[/tex] is:
B. [tex]\( w = 16 j \)[/tex]
