Answer :
Final answer:
To determine how many cups of pineapple juice Santana needs, a proportion can be set up using the given ratio of 5 tablespoons pineapple juice per 3 tablespoons of lemonade mix. Since there are 16 tablespoons in a cup, via conversion and multiplication, it is determined that Santana needs 20 cups of pineapple juice for her party punch.
Explanation:
Santana wants to make a large pitcher of punch for a party with 12 cups of lemonade mix. The ratio given for the punch is 5 tablespoons of pineapple juice per 3 tablespoons of lemonade mix. To calculate the amount of pineapple juice needed, we need to set up a proportion based on the ratio and the given quantity of lemonade mix.
Firstly, it's important to understand that there are 16 tablespoons in 1 cup. Using the given ratio, we can calculate the number of tablespoons of pineapple juice needed for one cup of lemonade mix:
- 3 tablespoons lemonade mix corresponds to 5 tablespoons pineapple juice.
- 16 tablespoons lemonade mix (1 cup) corresponds to (5/3) * 16 tablespoons pineapple juice.
- So, 1 cup of lemonade mix requires (5/3) * 16 = 26.67 tablespoons of pineapple juice.
Next, we calculate the total amount of pineapple juice needed for 12 cups of lemonade mix:
- 12 cups of lemonade mix requires 12 * 26.67 tablespoons of pineapple juice.
- That equals 320.04 tablespoons of pineapple juice.
- Finally, convert tablespoons to cups by dividing by 16:
- 320.04 tablespoons / 16 tablespoons per cup = 20 cups of pineapple juice.
Therefore, Santana will need 20 cups of pineapple juice for her party punch.
