Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 160 pints of a mixture that is 80% pure fruit juice?

Answer 1

Answer: There are 32 pints of first type and 128 pints of second type in mixture.

Step-by-step explanation:

Since we have given that

Percentage of pure fruit juice in first type = 60%

Percentage of pure fruit juice in second type = 85%

Percentage of pure fruit juice in mixture = 80%

We will use "Mixture and Allegation" to find the ratio of first and second type in mixture:

          First type          Second type

               60%                    85%

                              80%

------------------------------------------------------------------------

     85-80               :              80-60

       5%                  :                 20%

        1                     :                   4

so, the ratio of first and second type is 1:4.

Total number of pints of mixture = 160

Number of pints of mixture of  first type in mixture  is given by

$\dfrac{1}{5}\times 160\\\\=32\ pints$

Number of pints of mixture of second type in mixture is given by

$\dfrac{4}{5}\times 160\\\\=4\times 32\\\\=128\ pints$

Hence, there are 32 pints of first type and 128 pints of second type in mixture.