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?

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windyyork windyyork · Answer 1 · 2019-07-08T07:33:31+02:00

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

[tex]\dfrac{1}{5}\times 160\\\\=32\ pints[/tex]

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

[tex]\dfrac{4}{5}\times 160\\\\=4\times 32\\\\=128\ pints[/tex]

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