One canned juice drink is 20% orange juice! another is 5% orange juice. How many liters of each should be mixed together in order to get 15L that is 16% orange juice?

amount of 20% juice used ...... x L

amount of 5% juice used ....... 15 - x L

.20x + .05(15-x) = .16(15)
times 100 to get rid of those decimals
20x + 5(15-x) = 16(15)
20x + 75 - 5x = 240
15x = 165
x = 11

Answer as needed.

To solve this problem, let's denote the amount of the 20% orange juice drink as x liters and the amount of the 5% orange juice drink as y liters.

Now, let's break down the problem one step at a time:

Step 1: Set up an equation based on the amount of orange juice in each juice drink.
The amount of orange juice in the 20% orange juice drink is 20% of x liters, which can be expressed as 0.2x liters.
Similarly, the amount of orange juice in the 5% orange juice drink is 5% of y liters, which can be expressed as 0.05y liters.

Step 2: Write an equation based on the total amount of the mixture.
The total volume of the mixture is 15 liters, so the sum of the amounts of the two juice drinks should be equal to 15 liters: x + y = 15.

Step 3: Write an equation based on the concentration of orange juice in the mixture.
The mixture should contain 16% orange juice, which can be expressed as 0.16 multiplied by the total volume of the mixture (15 liters): 0.16 * 15 = 0.2x + 0.05y.

Now, we have a system of two equations:
x + y = 15 (equation 1)
0.2x + 0.05y = 0.16 * 15 (equation 2)

To solve this system of equations, we can use the substitution method or elimination method. Let's use the elimination method to solve it:

Multiply equation 1 by 0.05 to eliminate y:
0.05x + 0.05y = 0.05 * 15

Subtract this equation from equation 2 to eliminate y:
(0.2x + 0.05y) - (0.05x + 0.05y) = 0.16 * 15 - 0.05 * 15

Simplify the equation:
0.15x = 0.16 * 15 - 0.05 * 15

Calculate the right side of the equation:
0.15x = 2.4 - 0.75
0.15x = 1.65

Divide both sides of the equation by 0.15 to solve for x:
x = 1.65 / 0.15
x = 11

Now substitute the value of x in equation 1 to find y:
11 + y = 15
y = 15 - 11
y = 4

Therefore, you would need 11 liters of the 20% orange juice drink and 4 liters of the 5% orange juice drink to make 15 liters of a mixture that is 16% orange juice.