Three-Step-Problem...A punch recipe says to mix 4 cups pineapple juice, 8 cups orange juice, and 12 cups seltzer in order to make 18 servings of punch.
a)How many cups of each ingredient do you need to make 108 cups of punch?
b)How many servings can be made from 108 cups of punch?
c)For every cup of seltzer you use, how much orange juice do you use?
THANK YOU!!
a.
24 cups pineapple juice
48 cups orange juice
72 cups seltzer
b. 6
c. 0.6(6)
b and c are wrong
A is wrong too.
Wrong answers
To solve this three-step problem, we'll break it down into three separate steps:
1) Find the ratio of ingredients per serving.
2) Use the ratio to find the quantity of ingredients needed for 108 cups of punch.
3) Calculate the number of servings that can be made from 108 cups of punch and the ratio of seltzer to orange juice.
Let's begin:
Step 1: Find the ratio of ingredients per serving:
The given recipe states that to make 18 servings of punch, you need 4 cups of pineapple juice, 8 cups of orange juice, and 12 cups of seltzer. We can express this ratio as:
Pineapple juice : Orange juice : Seltzer = 4 : 8 : 12
Step 2: Use the ratio to find the quantity of ingredients needed for 108 cups of punch:
To figure out how much of each ingredient is needed for 108 cups of punch, we need to scale the ratio up by a factor of 108/18 = 6. This means multiplying each number in the ratio by 6:
Pineapple juice = 4 cups * 6 = 24 cups
Orange juice = 8 cups * 6 = 48 cups
Seltzer = 12 cups * 6 = 72 cups
So, to make 108 cups of punch, you will need:
24 cups of pineapple juice
48 cups of orange juice
72 cups of seltzer
Step 3: Calculate the number of servings that can be made from 108 cups of punch and the ratio of seltzer to orange juice:
From the original recipe, we know that 18 servings can be made from the given quantities. So, to find the number of servings that can be made from 108 cups of punch, we divide 108 by the total number of cups per serving:
Number of servings = 108 cups / (4 cups + 8 cups + 12 cups) = 108 / 24 = 4.5 servings
Therefore, you can make 4.5 servings of punch from 108 cups of punch.
Finally, for every cup of seltzer used, the given recipe uses 1 cup of orange juice. This is derived from the ratio of seltzer to orange juice, which is 12 cups : 8 cups. So, for every 1 cup of seltzer, you will use 1 cup of orange juice.
I hope this helps! Let me know if you have any further questions.