In order to get a solution that contains 5% juice, 20 gallons of pure water should be added
a. The amount of juice in the original solution is 1.5 gallons
b. Original amount of solution is 10 gallons
c. No juice is added
d. 20 gallons solution (pure water) is added
From dilution formula
[tex]C_{1}V_{1} = C_{2}V_{2}[/tex]
Where [tex]C_{1}[/tex] is the initial concentration
[tex]V_{1}[/tex] is the initial volume
[tex]C_{2}[/tex] is the final concentration
[tex]V_{2}[/tex] is the final volume
From the question, [tex]C_{1}[/tex] = 15%, [tex]V_{1}[/tex] = 10 gallons, [tex]C_{2}[/tex] = 5% and [tex]V_{2}[/tex] is unknown
Putting these values into the formula, we get
15% × 10 = 5% × [tex]V_{2}[/tex]
150 = 5 × [tex]V_{2}[/tex]
[tex]V_{2}[/tex] = 150/5
[tex]V_{2}[/tex] = 30 gallons
This means the final volume of the solution to give a concentration of 5% will be 30 gallons
Gallons of pure water added = [tex]V_{2}[/tex] - [tex]V_{1}[/tex]
Gallons of pure water added = 30 gallons - 10 gallons
Gallons of pure water added = 20 gallons
Hence, In order to get a solution that contains 5% juice, 20 gallons of pure water should be added.
For the amount of juice in the original solution,
The volume of the original solution is 10 gallons and it contains 15% juice.
∴ Amount of juice in the original solution = 15% × 10
Amount of juice in the original solution = [tex]\frac{15}{100}\times 10[/tex]
Amount of juice in the original solution = [tex]\frac{150}{100}[/tex]
Amount of juice in the original solution = 1.5 gallons
Hence, the amount of juice in the original solution is 1.5 gallons
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