Question

250 mililiters of lemonade
500 mililiters of orange juice
250 mililiters of grape juice
250 mililiters of apple juice
500 mililiters of pineapple juice
500 mililters 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

To create exactly 5 liters of fruit punch, the total volume of juices needed must add up to 5000 milliliters (5 liters).

Let x be the number of containers needed for lemonade, y be the number of containers needed for orange juice, and z be the number of containers needed for grape juice.

Based on the given volumes of each juice, we can write the following equations:
250x + 500y + 250z + 250 + 500 + 500 = 5000

Simplifying the equation:
250x + 500y + 250z = 4500

Since we are trying to find integer values for x, y, and z, we can divide the equation by 250 to eliminate the decimal:
x + 2y + z = 18

Given that we need at least three juices in our fruit punch recipe, we can select orange juice, grape juice, and pineapple juice to create a delicious brunch punch.

From the equations:
x = 18 - 2y - z

Let's try out different values for y and z to find integer solutions for x, y, and z.

For y = 1 and z = 0:
x = 18 - 2(1) - 0 = 16

Therefore, we need 16 containers of lemonade, 1 container of orange juice, and 0 containers of grape juice to make exactly 5 liters of fruit punch.