A pineapple drink contains 15% pineapple juice. How much pure pineapple juice should be added to 8 quarts of the drink to obtain a mixture containing 50% pineapple juice.

To solve this problem, we need to determine how much pure pineapple juice should be added to the existing pineapple drink to obtain a mixture containing 50% pineapple juice. Let's break it down step by step:

Step 1: Determine the amount of pineapple juice in the existing drink.
8 quarts of the drink contain 15% pineapple juice. To calculate the amount of pineapple juice in the existing drink, we multiply the volume of the drink (8 quarts) by the concentration of pineapple juice (15%):
Amount of pineapple juice in the existing drink = 8 quarts * 15% = 1.2 quarts

Step 2: Determine the final volume of the mixture.
Since we are adding pure pineapple juice to the existing drink, the final volume of the mixture will be the sum of the existing drink and the pure pineapple juice added. As per the problem statement, there are 8 quarts of the drink, and we need to calculate the total volume of the mixture after adding pure pineapple juice.

Step 3: Determine the pure pineapple juice required.
Let x denote the volume of pure pineapple juice to be added.

According to the problem, the mixture should contain 50% pineapple juice. This means that the amount of pineapple juice in the mixture should be equal to half the total volume of the mixture:
Amount of pineapple juice in the mixture = 0.5 * (8 + x)

Since we want the amount of pineapple juice in the mixture to be equal to the sum of the amount of pineapple juice in the existing drink and the pure pineapple juice added, we can set up the following equation:
1.2 quarts + x = 0.5 * (8 + x)

Step 4: Solve the equation.
Let's solve the equation from Step 3 to find the value of x:
1.2 + x = 0.5 * (8 + x)

Expanding the right side of the equation:
1.2 + x = 4 + 0.5x

Combining like terms by subtracting 0.5x from both sides:
1.2 + 0.5x = 4

Subtracting 1.2 from both sides:
0.5x = 2.8

Dividing both sides by 0.5:
x = 5.6

Step 5: Interpret the solution.
The solution x = 5.6 represents the volume of pure pineapple juice (in quarts) that should be added to the existing 8 quarts of the drink to obtain a mixture containing 50% pineapple juice.

.15*8+X=.5(8+X)

1.2+X=4+.5X
X-.5X=4-1.2
.5X=2.8
X=2.8/.5
X=5.6 QTS. OF PURE PINEAPPLE JUICE IS USED.
PROOF:
.15*8+5.6=.5(8+5.6)
1.2+5.6=.5*13.6
6.8=6.8

How many quarts of pure pineapple juice should Theo add to a 20% pineapple drink to create 5 quarts of 50% of pineapple juice mixture?

To solve this problem, we need to find out how much pure pineapple juice should be added to the existing 8 quarts of the 15% pineapple drink to obtain a mixture containing 50% pineapple juice.

Let's break down the problem step by step:

Step 1: Determine the amount of pure pineapple juice in the starting mixture.
The starting mixture is 8 quarts of 15% pineapple juice. To find the amount of pure pineapple juice, we need to calculate 15% of 8 quarts:

Amount of pineapple juice in the starting mixture = 8 quarts * 0.15 (15% expressed as a decimal)
Amount of pineapple juice in the starting mixture = 1.2 quarts

So, in the 8 quarts of the starting mixture, there is 1.2 quarts of pure pineapple juice.

Step 2: Determine the amount of pure pineapple juice needed in the final mixture.
Since we want a final mixture that contains 50% pineapple juice, we need to calculate the desired amount of pure pineapple juice:

Amount of pineapple juice needed in the final mixture = Total amount of mixture * Desired percentage of pineapple juice
Amount of pineapple juice needed in the final mixture = (8 quarts + x quarts) * 0.50 (50% expressed as a decimal)

Here, x represents the amount of pure pineapple juice we need to add.

Step 3: Set up an equation with the amount of pure pineapple juice.
Now, we can set up an equation using the amount of pure pineapple juice in the starting mixture and the amount of pure pineapple juice needed in the final mixture:

Amount of pineapple juice in the starting mixture + Amount of pineapple juice added = Amount of pineapple juice needed in the final mixture

1.2 quarts + x quarts = (8 quarts + x quarts) * 0.50

Step 4: Solve the equation.
Let's solve the equation to find the value of x.

1.2 quarts + x quarts = (8 quarts + x quarts) * 0.50
1.2 + x = 4 + 0.5x

Now, we'll isolate the x term:
x - 0.5x = 4 - 1.2
0.5x = 2.8

Simplifying further:
x = (2.8) / 0.5
x = 5.6

Therefore, you will need to add 5.6 quarts of pure pineapple juice to the 8 quarts of the 15% pineapple drink to obtain a mixture containing 50% pineapple juice.