Juice Containers: 250 milliliters of lemonade; 500 milliliters of orange juice; 250 milliliters of grape juice; 250 milliliters of apple juice; 500 milliliters of pineapple juice; and 500 milliliters of cranberry juice. Design your own fruit punch recipe for brunch! Your recipe must create exactly 5 liters of punch and include at least three of the juices. also be sure to include how many containers of each juice you need. Show your work by writing equations that show how you determined the capacity.

Question

Juice Containers: 250 milliliters of lemonade; 500 milliliters of orange juice; 250 milliliters of grape juice; 250 milliliters of apple juice; 500 milliliters of pineapple juice; and 500 milliliters of cranberry juice. Design your own fruit punch recipe for brunch! Your recipe must create exactly 5 liters of punch and include at least three of the juices. also be sure to include how many containers of each juice you need. Show your work by writing equations that show how you determined the capacity.

Answer 1

Let's design a fruit punch recipe using lemonade, orange juice, and pineapple juice.

To create exactly 5 liters of punch, we need to determine the number of containers of each juice we would need considering that:

1 container of lemonade = 250 mL
1 container of orange juice = 500 mL
1 container of pineapple juice = 500 mL

Let x be the number of containers of lemonade, y be the number of containers of orange juice, and z be the number of containers of pineapple juice.

The total capacity of the punch should equal 5 liters or 5000 milliliters:

250x + 500y + 500z = 5000

Now we will choose the number of containers for each juice. Let's have 6 containers of lemonade, 4 containers of orange juice, and 4 containers of pineapple juice:

250(6) + 500(4) + 500(4) = 5000
1500 + 2000 + 2000 = 5500

This exceeds our desired 5 liters capacity, so we need to adjust the quantities.

Let's try 4 containers of lemonade, 4 containers of orange juice, and 3 containers of pineapple juice:

250(4) + 500(4) + 500(3) = 5000
1000 + 2000 + 1500 = 4500

This is less than our desired 5 liters capacity, so we will further adjust the quantities.

Let's try 8 containers of lemonade, 3 containers of orange juice, and 3 containers of pineapple juice:

250(8) + 500(3) + 500(3) = 5000
2000 + 1500 + 1500 = 5000

Success! We have met our desired 5 liters capacity with these quantities.

Our fruit punch recipe is as follows:
- 8 containers of lemonade (2000 mL)
- 3 containers of orange juice (1500 mL)
- 3 containers of pineapple juice (1500 mL)

This will create a 5-liter (5000 mL) fruit punch, including 3 types of juices.