)ne canned juice drink is 25% orange juice; another is 55% orange juice. How many liters of each should be mixed together in order to get 20L that is 21% orange juice?
if there are x liters of 25% juice, then there are (20-x) of 55% juice. So,
.25x + .55(20-x) = .21(20)
To find out how many liters of each juice drink should be mixed, we can set up an equation based on the given information.
Let's assume the number of liters of the 25% orange juice drink is x, and the number of liters of the 55% orange juice drink is y.
Given:
1. The total amount of juice we want to obtain is 20 liters.
2. The desired orange juice concentration we want is 21%.
Now, we can set up the equation based on the amount of orange juice in the mixture:
0.25x + 0.55y = 0.21(20) (Equation 1).
Explanation:
The left side of the equation represents the total amount of orange juice in the mixture.
The right side of the equation represents the desired concentration of orange juice in the final mixture (0.21 or 21% of 20 liters).
Now, we need another equation to solve for the variables x and y. Since we have two unknowns, we need one more equation.
The second equation is based on the total amount of liquid in the mixture:
x + y = 20 (Equation 2).
Explanation:
The left side of the equation represents the total amount of liquid when the two juices are mixed.
The right side of the equation represents the total amount of liquid we want, which is 20 liters.
Now, we have a system of two equations with two unknowns (Equations 1 and 2):
0.25x + 0.55y = 4.2 (Equation 1)
x + y = 20 (Equation 2)
To solve this system of equations, we can use substitution or elimination method.
Let's use the substitution method:
Rearranging Equation 2, we get:
x = 20 - y
Substitute this value of x into Equation 1:
0.25(20 - y) + 0.55y = 4.2
Now we can solve for y:
5 - 0.25y + 0.55y = 4.2
0.30y = 4.2 - 5
0.30y = -0.8
y = -0.8 / 0.30
y ≈ 2.66 liters
Now, substitute the value of y back into Equation 2 to solve for x:
x + 2.66 = 20
x = 20 - 2.66
x ≈ 17.34 liters
Therefore, to obtain a 20-liter mixture with a 21% orange juice concentration, you should mix approximately 17.34 liters of the 25% orange juice drink with 2.66 liters of the 55% orange juice drink.