one canned jucie drink is 15% orange jucie; another is 10% orange jucie. How many liters of each should be mixed together in order to get 5L that is 11% orange jucie?
How many liter of the 15% orange jucie and how many liters of the 10% orange jucie should be in this mixture
To solve this problem, we need to set up an equation based on the given information.
Let's assume we need to mix x liters of the 15% orange juice and y liters of the 10% orange juice to obtain 5 liters of a mixture with 11% orange juice.
The equation for the total quantity of orange juice in the mixture can be derived as follows:
0.15x + 0.10y = 0.11 * 5
Now, we can solve this equation to find the values of x and y.
0.15x + 0.10y = 0.55
To make it easier to work with, we can multiply the equation by 100 to remove the decimals:
15x + 10y = 55
We also know that the total quantity of the mixture is 5 liters:
x + y = 5
We have two equations:
15x + 10y = 55
x + y = 5
We can use substitution or elimination to solve these equations. Let's use the elimination method to eliminate y:
Multiply the second equation by -10:
-10x - 10y = -50
Add this equation to the first equation:
15x + 10y - 10x - 10y = 55 - 50
Simplify:
5x = 5
Divide by 5:
x = 1
Now, substitute the value of x into the second equation to find y:
1 + y = 5
y = 5 - 1
y = 4
Therefore, we need to mix 1 liter of the 15% orange juice with 4 liters of the 10% orange juice to get a 5-liter mixture with 11% orange juice.