Pineapple juice

Question

You have 6 liters of a pineapple juice blend that has 50% pure pineapple juice. How many liters of pure pineapple juice needs to be added to make a juice blend that is 75% pineapple juice?

Answer 1

One way to solve this is by the use of a process called "alligation".  It uses a grid of HAVE...WANT...NEED set up as follows

where you cross subtract what you have from what you want to get what you need.  

HAVE......WANT......NEED

50%......................25....

...............75%..............

100%....................25....

 

Thus you would need 25 parts of the 50% and 25 parts of the 100% (pure juice) to make 50 parts of the 75%.  Since you have 6 liters of the 50%, that is equal to 25 parts, and so 25 parts of the 100% will also be 6 liters.

 

Using more traditional algebra:

(6 L)(50%) + (x L)(100%) = (6L + xL)(75%)

300 + 100x = 450 + 75x

25x = 150

x = 6 liters of pure juice needs to be added