Question

An advertisement for an orange drink claims that the drink contain 10% orange juice. How much pure orange juice would have to be added to the drink to obtain 5 quart a mixture containing 40% orange juice?

Answer 1

Answer: The amount of pure orange juice that needs to be added is 2.5 quarts

Explanation:

We are given:

Amount of orange juice added in 10% solution = 5 quarts

So, total amount of orange juice added =
`(10)/(100)* 5=0.5` quarts

We need to find:

The amount of pure orange juice added in 40 % solution

Let the amount of pure orange juice added be 'x' quarts

Calculating the amount of pure orange juice added:

Amount of pure juice in 10% solution plus the amount of pure juice added will be equal to the amount of pure juice added in 40 % solution

Amount of pure juice added in 40 % solution =
`(40)/(100)* (5+x)=0.4(5+x)`

Expression becomes:

`0.5+x=0.4(5+x)\\\\0.5+x=2+0.4x\\\\x==(1.5)/(0.6)=2.5`

Hence, the amount of pure orange juice that needs to be added is 2.5 quarts