SOLUTION: A container is filled with 72 litres of orange juice. Twenty-four litres of orange juice are removed and the container is refilled with lemon juice. The contents of the mixture are

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A container is filled with 72 litres of orange juice. Twenty-four litres of orange juice are removed and the container is refilled with lemon juice. The contents of the mixture are      Log On


   

Question 1120048: A container is filled with 72 litres of orange juice. Twenty-four litres of orange juice are removed and the container is refilled with lemon juice. The contents of the mixture are thoroughly mixed and 24 litres of the mixture is removed and the container is again refilled with lemon juice. What is the ratio of orange juice to lemon juice in the final mixture?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you started with 72 ounces of orange.

you took out 24 ounces of orange juice and replaced it with 24 ounces of lemon juice.

you now had 48 ounces of orange juice and 24 ounces of lemon juice.

you took out 24 ounces of this mixture.

since the ratio of orange juice to lemon juice was now 48/24 = 2/1, the ratio of orange juice to the total was 2/(2+1) = 2/3.

2/3 * 24 = 16.
1/3 * 24 = 8.

24 ounces of the mixture was composed of 16 ounces of orange juice and 8 ounces of lemon juice.

you replaced 16 ounces of orange juice and 8 ounces of lemon juice with 24 ounces of lemon juice.

you now had 48 minus 16 = 32 ounces of orange juice.

you now had 24 minus 8 plus 24 = 40 ounces of lemon juice.

your mixture now contains 32 ounces of orange juice and 40 ounces of lemon juice.

the ratio of orange juice to lemon juice is now 32/40 = 4/5.

the ratio of orange juice to total mixture is now 32/(32+40) = 32/72 = 4/9.

your solution is that the final mixture has an orange to lemon juice ratio of 4/5.


Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
A container is filled with 72 litres of orange juice.
Twenty-four litres of orange juice are removed and the container is refilled with lemon juice.
The contents of the mixture are thoroughly mixed and 24 litres of the mixture is removed and
the container is again refilled with lemon juice. What is the ratio of orange juice to lemon juice in the final mixture?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  The container is filled with 72 liters of orange juice. 


2.  24 liters of orange juice are removed.  

        72 - 24 = 48 liters of orange juice remained.


3.  Then 24 liters of lemon juice refilled.

        Now we have 72 liters of the mixture; 

            of them, 48 liters of orange juice and 24 liters lemon juice, in proportion 2 parts of the O-juice to 1 part of the L-juice.


4.  Next, 24 liters of the mixture removed.

       Of them,  16 liters of the O-juice removed and 8 liters of the L-juice removed, in the same proportion.


5.  Now we have  48-16 = 32 liters of the O-juice  and  24-8 = 16 liters  of the mixture.


6.  Next 24 liters of the L-juice refilled.

       Now we have 32 liters of the O-juice and  16+24 = 40 liters of the L-juice: in all 32 + 40 = 72 liters of the new mixture.


7.  The ratio of the O-juice to L-juice in the final mixture is  32%2F40 = 4%2F5.


Answer.  The ratio under the question is  4%2F5.

Solved.