How much of a 60% orange juice drink must be mixed with 30 gallons of a 10% orange juice drink to obtain a mixture that is 50% orange juice.
.6x + .1(30) = .5(x+30)
x = 120
To solve this problem, we can set up an equation based on the amount of orange juice in each mixture. Let's assume you'll be mixing x gallons of the 60% orange juice drink.
The 60% orange juice drink contains 60% orange juice, which means it has 0.6 * x gallons of orange juice.
The 30-gallon 10% orange juice drink contains 10% orange juice, so it has 0.1 * 30 = 3 gallons of orange juice.
For the final mixture to be 50% orange juice, the total amount of orange juice in the x gallons of 60% orange juice and the 30 gallons of 10% orange juice must equal 50% of the total volume of the mixture.
0.6x + 3 = 0.5(x + 30)
Solving this equation will give us the value of x:
0.6x + 3 = 0.5x + 15
0.6x - 0.5x = 15 - 3
0.1x = 12
x = 12 / 0.1
x = 120
Therefore, you will need to mix 120 gallons of the 60% orange juice drink with the 30 gallons of the 10% orange juice drink to obtain a mixture that is 50% orange juice.
To solve this problem, you can use the concept of weighted averages. Let's break it down step by step:
1. Determine the amount of 60% orange juice drink needed.
Let's say x gallons of the 60% orange juice drink are needed.
2. Calculate the amount of pure orange juice in the 60% orange juice drink.
Since the 60% orange juice drink is 60% orange juice, the amount of pure orange juice in x gallons would be 0.6x gallons.
3. Calculate the amount of pure orange juice in the 10% orange juice drink.
In 30 gallons of the 10% orange juice drink, the amount of pure orange juice would be 0.1 * 30 = 3 gallons.
4. Set up the equation based on the desired mixture.
The total amount of pure orange juice in the final mixture should be equal to the sum of pure orange juice from the two initial drinks. In this case, it can be written as:
0.6x + 3 = 0.5 * (30 + x)
5. Solve the equation.
Simplify the equation:
0.6x + 3 = 15 + 0.5x
Combine like terms:
0.6x - 0.5x = 15 - 3
0.1x = 12
Divide by 0.1:
x = 120
6. Answer the question.
To obtain a mixture that is 50% orange juice, you need to mix 120 gallons of the 60% orange juice drink with 30 gallons of the 10% orange juice drink.
Therefore, you must mix 120 gallons of the 60% orange juice drink with 30 gallons of the 10% orange juice drink to obtain a mixture that is 50% orange juice.