Question

Bethany is making punch. She uses 2 cups of orange juice for every 3 cups of cranberry juice.She wants to make enough punch for 60 people to each have a half cup serving. How many cups of orange juice and cranberry juice will she need to combine? Explain

Answer 1

18 cups of cranberry juice and 12 cups of orange juice to make enough punch for 60 people.

Explanation

To determine how many cups of orange juice and cranberry juice Bethany needs to combine, we can use the given ratio of the two juices, which is 2 cups of orange juice for every 3 cups of cranberry juice. Let's assume that x cups of cranberry juice are needed. Then, we can find the amount of orange juice needed by multiplying x by the ratio of orange juice to cranberry juice, which is 2/3. Thus, the amount of orange juice needed is (2/3)x.

To find the total amount of punch needed, we can multiply the serving size (0.5 cups) by the number of people (60), which gives us 30 cups.

To find the total amount of cranberry juice needed, we can set up the equation:

x + (2/3)x = 30

Simplifying this equation, we get:

(5/3)x = 30

Dividing both sides by 5/3, we get:

x = 18

Therefore, Bethany needs 18 cups of cranberry juice and (2/3) * 18 = 12 cups of orange juice to make enough punch for 60 people.

Answer 2

12 cups of orange juice and 18 cups of cranberry juice

Explanation:

First, let's determine the number of cups used in the recipe.

2 cups of orange juice + 3 cups of cranberry juice = 5 cups

Now, if every person only has 0.5 cups of juice, how many people can drink 5 cups of juice?

5 / 0.5 = 10

If one batch is enough for 10 people, how many batches will we need for 60 people?

60 / 10 = 6

So, we will need to make the recipe 6 times in order to make enough punch for everyone.

Lastly, let's mutliply the recipe by 6.

6 * (2 cups of orange juice + 3 cups of cranberry juice)

12 cups of orange juice + 18 cups of cranberry juice

So, Bethany will need 12 cups of orange juice and 18 cups of cranberry juice to make enough punch for 60 people to have 0.5 cups of punch.

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