One canned juice drink is 25% orange juice another is 5% orange juice. How many liters of each should be mixed together in order to get 20L that is 24% orange juice?
How many liters of the 25% orange juice should be in mixture?
How many liters of the 5% orange juice should be in mixture?
How can I solve this problem, or what is the best method??
Let V be the volume of the 25% orange juice.
Since the total volume is 20 l, the volume of 5% orange juice is (20-V).
The resulting mixture is 24%, therefore
25%*V + 5%*(20-V) = 24%*20
Can you solve for V? (It is a whole number close to 20).
To solve this problem, you can use a method known as the "mixture" or "allegation" method. This involves setting up a ratio based on the concentrations and quantities of the two juices.
Let's say you want to mix x liters of the 25% orange juice and y liters of the 5% orange juice to obtain a total of 20 liters that is 24% orange juice.
First, let's set up the equation for the total amount of orange juice in the mixture:
0.25x + 0.05y = 0.24(20)
Simplifying this equation, we have:
0.25x + 0.05y = 4.8
Next, we need to set up a ratio based on the concentration of orange juice:
x/y = (0.24 - 0.05)/(0.25 - 0.24) = 19/1
Now we have a system of two equations:
0.25x + 0.05y = 4.8 (equation 1)
x/y = 19/1 (equation 2)
To solve this system, we can use substitution or elimination method.
Substitution method:
From equation 2, we have x = 19y.
Substituting this value into equation 1, we get:
0.25(19y) + 0.05y = 4.8
4.75y + 0.05y = 4.8
4.8y = 4.8
y = 1
Now, substitute this value of y back into equation 2 to find x:
x/1 = 19/1
x = 19
Therefore, you should mix 19 liters of the 25% orange juice and 1 liter of the 5% orange juice to obtain the desired 20 liters that is 24% orange juice.