Translate to a system of equations but do not solve.
One canned juice drink is 20% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 10L that is 13% orange juice?
How many liters of the 20% orange juice should be in the mixture?
How many liters of the 10% orange juice should be in the mixture?
To translate the problem into a system of equations, we can start by assigning variables to the unknown quantities. Let's call the number of liters of the 20% orange juice "x" and the number of liters of the 10% orange juice "y" that should be mixed together.
Based on the given information, we can write two equations:
Equation 1: The total volume of the mixture should be 10L.
x + y = 10
Equation 2: The percentage of orange juice in the mixture should be 13%.
(0.20x + 0.10y) / 10 = 0.13
In Equation 2, we use the percentages given for the orange juice content (20% and 10%), and we divide the sum of the orange juice quantities for each type of juice (0.20x + 0.10y) by the total volume of the mixture (10L), which should be equal to 13% (0.13) of orange juice.
Therefore, the system of equations would be:
x + y = 10
(0.20x + 0.10y) / 10 = 0.13
These equations represent the problem mathematically without solving for the actual values of x and y.