If 500 L of a juice drink is12% orange juice, how many liters of pure orange juice should be added to make a drink that is 20% orange juice

Question

how do I do it?

Answer 1

The solution offered by Thomas Z. is not correct. If you add 40 L of pure orange juice to a 12% orange juice solution, then you will have 100 liters of juice out of 540 total liters. This is not 20%, but approximately 18.5%

 

Here is a correct solution (pun intended):

 

Allow X to represent the amount of pure OJ to be added. In the original mixture, there are 60 L of juice in a 500 L solution since 12% of 500 = 60.

 

So, the fraction 60/500 represents the original mixture. Notice that the numerator represents the amount of juice while the denominator represents the total amount. When we add X liters of pure OJ this amount must be added to the numerator because it is pure juice. It must also be added to the denominator because it does add to the total volume as well.

 

Now, (60+X)/(500+X) = 0.20 because after adding this unknown amount of pure OJ we now have a solution that is 20% orange juice.

 

If (60+x)/(500+x) = 0.20 or 1/5.  Cross-multiply to obtain 500+x = 5(60+x) = 300 + 5x

If 500 + x = 300 + 5x then subtract X from both sides and also subtract 300 from both sides to obtain 4x = 200

Finally divide both sides by 4 to obtain x = 50.

 

You must add 50 L of pure OJ to a 500 L of drink which is 60 L of OJ to create 110L of OJ out of 550 L of drink.

20% of 550 is 110.

 

That is my solution (pun intended again).

 

 

 

Answer 2

First, find how many liters 12% is.

500*12%= 60L

 

We need to find how many liters 8% is. So, if 12% = 60 L, then 4% = 20 L.

• Both 12 and 60 share a factor of 3, and a factor of 8 is 4. When we divide both 12 and 60 by 3, we get 4% = 20 L.
  
  

If 4% = 20, and we need to find 8%, then 8% must equal 40 L. 

 

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