Canned juice A is 25% orange juice, while canned juice B is 5% orange juice. How many liters of juice A should be used mixed with juice B in order to get 10 L that is 24% orange juice?
Let x be the number of liters of juice A and y be the number of liters of juice B.
We have the equation x + y = 10 because the total amount of juice should be 10 L.
We also have the equation 0.25x + 0.05y = 0.24 * 10 because the total amount of orange juice should be 24% of the total amount of juice.
Simplifying the second equation, we get 0.25x + 0.05y = 2.4.
Multiplying both sides of the first equation by 0.05 to eliminate y, we get 0.05x + 0.05y = 0.5.
Subtracting the second equation from the first equation, we get 0.2x = 1.9.
Dividing both sides of the equation by 0.2, we get x = 9.5.
Substituting this value back into the first equation, we get 9.5 + y = 10.
Subtracting 9.5 from both sides of the equation, we get y = 0.5.
Therefore, 9.5 liters of juice A should be used mixed with 0.5 liters of juice B to get 10 L that is 24% orange juice.
To find out how many liters of juice A should be used, we can set up a equation using the given information:
Let x be the number of liters of juice A.
Since the total volume of juice needed is 10 liters, the amount of juice B will be 10 - x.
Now let's set up the equation based on the concentration of orange juice:
0.25x + 0.05(10 - x) = 0.24(10)
0.25x + 0.5 - 0.05x = 2.4
Combine like terms:
0.2x + 0.5 = 2.4
Subtract 0.5 from both sides:
0.2x = 1.9
Divide both sides by 0.2:
x = 1.9 / 0.2
x = 9.5
Therefore, you would need 9.5 liters of juice A to mix with 0.5 liters of juice B in order to get 10 liters of juice that is 24% orange juice.