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Answer :
Let's figure out how many tablespoons of lemonade mix are needed per cup of sparkling water for each recipe:
a. For the first recipe, there are 4 tablespoons of lemonade mix and 12 cups of sparkling water. To find the number of tablespoons of lemonade mix per cup of water, we'll divide the number of tablespoons by the number of cups:
[tex]\[ \frac{4 \text{ tablespoons of mix}}{12 \text{ cups of water}} = \frac{1}{3} \][/tex]
So, it takes [tex]\( \frac{1}{3} \)[/tex] tablespoons of lemonade mix per cup of sparkling water.
b. In the second recipe, there are 4 tablespoons of lemonade mix and 6 cups of sparkling water. Again, divide the mix by the water:
[tex]\[ \frac{4 \text{ tablespoons of mix}}{6 \text{ cups of water}} = \frac{2}{3} \][/tex]
This means it takes [tex]\( \frac{2}{3} \)[/tex] tablespoons of lemonade mix per cup.
c. The third recipe uses 3 tablespoons of lemonade mix and 5 cups of sparkling water. We calculate:
[tex]\[ \frac{3 \text{ tablespoons of mix}}{5 \text{ cups of water}} = 0.6 \][/tex]
Therefore, it takes 0.6 tablespoons of lemonade mix per cup of sparkling water.
d. In the fourth recipe, there's [tex]\(\frac{1}{2}\)[/tex] tablespoon of lemonade mix for [tex]\(\frac{3}{4}\)[/tex] cups of sparkling water. Calculate it like this:
[tex]\[ \frac{\frac{1}{2} \text{ tablespoon of mix}}{\frac{3}{4} \text{ cups of water}} = \frac{1}{2} \times \frac{4}{3} = \frac{2}{3} \][/tex]
Thus, it takes [tex]\( \frac{2}{3} \)[/tex] tablespoons of lemonade mix per cup of sparkling water.
These calculations help us understand the amount of lemonade mix used in each recipe relative to the sparkling water.
a. For the first recipe, there are 4 tablespoons of lemonade mix and 12 cups of sparkling water. To find the number of tablespoons of lemonade mix per cup of water, we'll divide the number of tablespoons by the number of cups:
[tex]\[ \frac{4 \text{ tablespoons of mix}}{12 \text{ cups of water}} = \frac{1}{3} \][/tex]
So, it takes [tex]\( \frac{1}{3} \)[/tex] tablespoons of lemonade mix per cup of sparkling water.
b. In the second recipe, there are 4 tablespoons of lemonade mix and 6 cups of sparkling water. Again, divide the mix by the water:
[tex]\[ \frac{4 \text{ tablespoons of mix}}{6 \text{ cups of water}} = \frac{2}{3} \][/tex]
This means it takes [tex]\( \frac{2}{3} \)[/tex] tablespoons of lemonade mix per cup.
c. The third recipe uses 3 tablespoons of lemonade mix and 5 cups of sparkling water. We calculate:
[tex]\[ \frac{3 \text{ tablespoons of mix}}{5 \text{ cups of water}} = 0.6 \][/tex]
Therefore, it takes 0.6 tablespoons of lemonade mix per cup of sparkling water.
d. In the fourth recipe, there's [tex]\(\frac{1}{2}\)[/tex] tablespoon of lemonade mix for [tex]\(\frac{3}{4}\)[/tex] cups of sparkling water. Calculate it like this:
[tex]\[ \frac{\frac{1}{2} \text{ tablespoon of mix}}{\frac{3}{4} \text{ cups of water}} = \frac{1}{2} \times \frac{4}{3} = \frac{2}{3} \][/tex]
Thus, it takes [tex]\( \frac{2}{3} \)[/tex] tablespoons of lemonade mix per cup of sparkling water.
These calculations help us understand the amount of lemonade mix used in each recipe relative to the sparkling water.
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