One canned juice drink is 25 percent orange juice; another is 10 percent orange juice How many liters of each should be mixed together in order to get 15L that is 23 percent orange juice?
x and (15 - x are) the two amounts
oj = .25 x + .1 (15-x) = .23 (15)
solve for x and then also(15-x)
To determine the number of liters of each canned juice drink that should be mixed together in order to obtain a desired concentration of orange juice, we can use a system of equations. Let's denote the number of liters of the 25% orange juice drink as 'x' and the number of liters of the 10% orange juice drink as 'y'.
First, set up an equation to represent the total volume of the mixture:
x + y = 15 (since the total volume of the mixture is 15L)
Next, set up an equation to represent the desired concentration of orange juice:
(0.25x + 0.10y) / 15 = 0.23 (since the desired concentration of orange juice is 23%)
Now, we have a system of equations:
x + y = 15
(0.25x + 0.10y) / 15 = 0.23
To solve this system, we can use the substitution or elimination method. Let's use the elimination method.
Multiply the second equation by 15 to eliminate the denominator:
0.25x + 0.10y = 0.23 * 15
This simplifies to:
0.25x + 0.10y = 3.45
Now, multiply the first equation by 0.10 to get rid of the decimal coefficient:
0.10x + 0.10y = 1.5
Subtract this equation from the previous equation to eliminate 'y':
0.25x - 0.10x = 3.45 - 1.5
0.15x = 1.95
Divide both sides of the equation by 0.15:
x = 1.95 / 0.15
x = 13
Substitute the value of 'x' back into the first equation to solve for 'y':
13 + y = 15
y = 15 - 13
y = 2
Therefore, you should mix 13 liters of the 25% orange juice drink with 2 liters of the 10% orange juice drink to obtain 15 liters of a mixture that is 23% orange juice.