One canned juice drink is 15% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 5L that is 11% orange juice?
How many liters of the 15% orange juice should be in the mixture__ L ?
How many liters of the 10% orange juice should be in the mixture__ L ?
volume of 15% OJ --- x L
volume of 10% OH --- 5-x L
.15x + .1(5-x) = .11(5)
times 100 , don't like them decimals!
15x + 10(5-x) = 55
15x + 50 - 10x = 55
5x = 5
x = 1
So 1 L of the 15% stuff and
4 L of the 10% stuff
To solve this problem, we can use the concept of the concentration of a solution. The concentration of a solution is the amount of solute (in this case, orange juice) divided by the total volume of the solution.
We are given two types of canned juice drink: one with 15% orange juice and the other with 10% orange juice. We want to find out how many liters of each should be mixed together in order to obtain 5 liters of a solution with 11% orange juice.
Let's assume x liters of the 15% orange juice should be in the mixture, and therefore (5 - x) liters of the 10% orange juice should be in the mixture.
Now, let's calculate the amount of orange juice in each type of juice:
Amount of orange juice in the 15% orange juice = 0.15x liters
Amount of orange juice in the 10% orange juice = 0.10(5 - x) liters (since we have (5 - x) liters of the 10% orange juice)
To find the amount of orange juice in the mixture, we need to add these two amounts:
Amount of orange juice in the mixture = 0.15x + 0.10(5 - x)
Since we want 5 liters of the mixture to have an 11% concentration of orange juice, we can set up the following equation:
0.11(5) = 0.15x + 0.10(5 - x)
Simplifying the equation:
0.55 = 0.15x + 0.5 - 0.10x
Combining like terms:
0.55 - 0.5 = 0.15x - 0.10x
0.05 = 0.05x
Dividing both sides by 0.05:
x = 1
Therefore, 1 liter of the 15% orange juice should be in the mixture.
To find the amount of the 10% orange juice in the mixture, we can subtract the amount of the 15% orange juice we found:
5 - x = 5 - 1 = 4
Therefore, 4 liters of the 10% orange juice should be in the mixture.
So, the answers to the questions are:
How many liters of the 15% orange juice should be in the mixture? 1 liter
How many liters of the 10% orange juice should be in the mixture? 4 liters
To determine how many liters of each juice should be mixed together, we can set up a system of equations based on the given information.
Let's assume x liters of the 15% orange juice are required.
Therefore, the remaining volume of the mixture will be (5 - x) liters, which will be the amount of 10% orange juice.
Now, we can set up the equation for the orange juice concentration:
0.15x + 0.10(5 - x) = 0.11(5)
Simplifying the equation:
0.15x + 0.5 - 0.10x = 0.55
Combining like terms:
0.05x + 0.5 = 0.55
Subtracting 0.5 from both sides:
0.05x = 0.05
Dividing both sides by 0.05:
x = 1
So, 1 liter of the 15% orange juice should be in the mixture.
To find the amount of 10% orange juice:
5 - x = 5 - 1 = 4
Therefore, 4 liters of the 10% orange juice should be in the mixture.