Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 90 pints of a mixture that is 65% pure fruit juice?

Answer 1

let amount of 55% pure fruit juice used be x pints ,amount of 70% pure fruit juice used be y pints

90 pints of a mixture

=>x+y=90
=>y=90-x

90 pints of a mixture that is 65% pure fruit juice

=>0.55x+0.70y=0.65(90)
=>0.55x+0.70y=58.5

substitute y=90-x in 0.55x+0.70y=58.5

=>0.55x+0.70(90-x)=58.5
=>0.55x+63-0.70x=58.5
=>63-0.15x=58.5
=>0.15x=4.5
=>x=4.5_/0.15
=>x=30
substitute x=30 in y=90-x
=>y=90-30
=>y=60

30 pints of The first type(55% pure fruit juice), and 60 pints of the second type (70% pure fruit juice) must be used to make 90 pints of a mixture that is 65% pure fruit juice

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