Jan makes a party punch that requires 2 gallons of orange juice for every gallon of l 1/2 lemonade. Matt's favorite party punch recipe calls for 3 gallons of pineapple juice.
Is this addition or multiplication?? You didn't finish the problem.
To determine the amount of orange juice and lemonade needed for Matt's favorite party punch recipe, we can start by finding the ratio between orange juice and lemonade in Jan's party punch.
Jan's party punch requires 2 gallons of orange juice for every 1 1/2 gallons of lemonade. Let's convert 1 1/2 gallons to a mixed fraction:
1 1/2 = 3/2
So the ratio of orange juice to lemonade is 2:3/2, which can be simplified by multiplying both parts of the ratio by 2:
2 x 2 : (3/2) x 2
4 : 3
Therefore, the ratio of orange juice to lemonade for Jan's party punch is 4:3.
Now, we know that Matt's favorite party punch recipe requires 3 gallons of pineapple juice. Let's assume we need to use the same ratio of orange juice to lemonade as Jan's party punch.
To find the amount of orange juice needed, we'll set up a proportion using the ratios:
4/3 = x/3
To solve for x (the amount of orange juice needed), cross-multiply and solve for x:
4 * 3 = 3 * x
12 = 3x
Divide both sides of the equation by 3:
x = 12/3
x = 4
Therefore, Matt's favorite party punch recipe would require 4 gallons of orange juice.
To find out how much pineapple juice Matt's favorite party punch recipe requires, we need to compare the ratios of ingredients used in Jan's party punch and Matt's punch.
Jan's party punch requires 2 gallons of orange juice for every 1 1/2 gallons of lemonade.
Matt's party punch recipe calls for 3 gallons of pineapple juice.
Since the two recipes have a different base ingredient, we need to convert the ratios to a common base. In this case, we can convert them to a ratio of orange juice to pineapple juice.
Based on Jan's recipe, we know that 2 gallons of orange juice is equivalent to 1 1/2 gallons of lemonade. Let's calculate the ratio of orange juice to lemonade:
2 gallons orange juice : 1 1/2 gallons lemonade
To make the ratio easier to compute, let's convert 1 1/2 to an improper fraction:
2 gallons orange juice : 3/2 gallons lemonade
Now, since we want to find the ratio of orange juice to pineapple juice, we need to convert the ratio of orange juice to lemonade to a ratio of orange juice to pineapple juice.
To do this, we can set up a proportion:
2 gallons orange juice / x gallons pineapple juice = 3/2 gallons lemonade
Cross-multiplying, we get:
2 * (3/2) = x * 1
6/2 = x
Simplifying, we find that x = 3.
Therefore, based on the given information, Matt's favorite party punch recipe requires 3 gallons of pineapple juice.