One canned juice drink contains 30% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 20L that is 28% orange juice?
I want step by step help.
To solve this problem, we can use a method called the "mixture" or "weighted average" equation. We want to find the amount of each type of juice (30% and 10%) needed to create a mixture of 20L containing 28% orange juice.
Let's start by assigning variables:
Let x be the number of liters of the first juice (30% orange juice) that we will mix.
Then, (20 - x) will represent the number of liters of the second juice (10% orange juice) that we will mix.
Now, let's set up the equation:
Amount of orange juice from the first juice + Amount of orange juice from the second juice = Total amount of orange juice in the mixture.
To calculate the amount of orange juice from each juice:
For the first juice (30% orange juice): 0.30x (since it contains 30% orange juice).
For the second juice (10% orange juice): 0.10(20 - x) (since it contains 10% orange juice).
Therefore, our equation becomes:
0.30x + 0.10(20 - x) = 0.28(20).
Now, let's solve the equation step by step:
1. Distribute 0.10 to (20 - x):
0.30x + 0.10 * 20 - 0.10x = 0.28 * 20.
2. Simplify:
0.30x + 2 - 0.10x = 5.60.
3. Combine like terms:
0.20x + 2 = 5.60.
4. Subtract 2 from both sides:
0.20x = 3.60.
5. Divide both sides by 0.20:
x = 3.60 / 0.20.
6. Calculate:
x = 18.
So, 18 liters of the first juice (30% orange juice) should be mixed.
And the remaining amount is (20 - 18) = 2 liters of the second juice (10% orange juice).
Work with the amount of juice in each mixture. Add up the juice in the parts, and it must equal the juice in the final mixture. If there are x liters of 30% juice, there are 20-x liters of 10% juice:
.30x + .10(20-x) = .28(20)
just solve for x to answer the questions.