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?

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Genesis Rosario · Accepted Answer

Step 1let amount of 55% pure fruit juice used be x pints ,amount of 70% pure fruit juice used be y pints90 pints of a mixture  =&amp;gt;  x  +  y  =  90  ⇒  y  =  90  −  x90 pints of a mixture that is 65% pure fruit juice  ⇒  0.55  x  +  0.70  y  =  0.65  (  90  )  ⇒  0.55  x  +  0.70  y  =  58.5substitute   y  =  90  −  x     i  n     0.55  x  +  0.70  y  =  58.5  ⇒  0.55  x  +  0.70  (  90  −  x  )  =  58.5  ⇒  0.55  x  +  63  −  0.70  x  =  58.5  ⇒  63  −  0.15  x  =  58.5  ⇒  0.15  x  =  4.5  ⇒  x  =  4.5      /    0.15  ⇒  x  =  30substitute   x  =  30     i  n     y  =  90  −  x  ⇒  y  =  90  −  30  ⇒  y  =  6030 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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