Question

How many gallons of pure water should be added to 10 gallons of a solution containing 15 % juice so that the remaining solution contains 5 % juice? Fill in the table: What is the amount of juice in the original solution? a=. What is the original amount of solution in gallons? b =. How much juice is added? c= . How much total solution is added? d=.

Answer 1

To dilute a solution from 15% juice to 5% juice, 1.5 gallons of juice in 10 gallons of the solution is mixed with an additional 20 gallons of pure water, resulting in a total solution of 30 gallons.

Step-by-step explanation:

The question involves diluting a solution by adding more solvent to it to decrease the percentage concentration of the solute. The original solution contains 15% juice, and we want to dilute it to 5% juice.

• The amount of juice in the original solution (a) is 10 gallons * 15% = 1.5 gallons.
• The original amount of the solution in gallons (b) is 10 gallons.
• No extra juice is added, so the amount of juice added (c) is 0 gallons.
• To solve for how much pure water should be added (d), we set up the equation:
  
  (1.5 gallons) / (10 gallons + x gallons) = 5%,
  
  where x is the number of gallons of water to be added.
  
  After solving, x = 20 gallons of water.

The total solution after adding x gallons of water is 30 gallons.