Question

If a 5-gallon container of pure juice is added to a 5 gallon container of 10% juice, what percent of the mixture is pure juice? Write an equation and solve. Be sure to use a let statement.

Answer 1

55% of the mixture is pure juice

Explanation:

let us solve the question

∵ There is 5-gallon container of pure juice

- That means the concentration of juice is 100%

∵ There is 5-gallon container of 10% juice

- That means the concentration of juice is 10%

∵ The two 5-gallon will added

- That mean the total of mixture is 5 + 5 = 10 gallons

∵ The concentration of juice in the mixture = 100% of 5 + 10% of 5

∵ 100% =
`(100)/(100)` = 1

∵ 10% =
`(10)/(100)` = 0.2

∴ The concentration of juice in the mixture = 1(5) + 0.1(5)

∴ The concentration of juice in the mixture = 5 + 0.5

∴ The concentration of juice in the mixture = 5.5 gallons

∴ The pure juice in the mixture is 5.5 gallons

Percentage of pure juice in the mixture = (pure juice/mixture) × 100%

∵ % of pure juice =
`(5.5)/(10)` × 100%

∴ % of pure juice = 0.55 × 100%

∴ % of pure juice = 55%

∴ 55% of the mixture is pure juice