SOLUTION: The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produc

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produc      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1147232: The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 160 pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80% pints of a mixture that is pure fruit juice?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pints of 45% juice needed
Let +b+ = pints of 95% juice needed
-----------------------------------------------
(1) +.45a+%2B+.95b+=+160+
(2) +160+%2F+%28+a+%2B+b+%29+=+.8+
-----------------------------------
(1) +45a+%2B+95b+=+16000+
(1) +9a+%2B+19b+=+3200+
and
(2) +.8a+%2B+.8b+=+160+
(2) +8a+%2B+8b+=+1600+
(2) +a+%2B+b+=+200+
--------------------------------
Multiply both sides of (2) by +9+
and subtract (2) for (1)
(1) +9a+%2B+19b+=+3200+
(2) +-9a+-+9b+=+-1800+
--------------------------------
+10b+=+1400+
+b+=+140+
and
(2) +a+%2B+b+=+200+
(2) +a+%2B+140+=+200+
(2) +a+=+60+
-----------------------
60 pints of 45% juice are needed
140 pints of 95% juice are needed
---------------------------------------------
check:
(1) +.45a+%2B+.95b+=+160+
(1) +.45%2A60+%2B+.95%2A140+=+160+
(1) +27+%2B+133+=+160+
(1) +160+=+160+
OK
get a 2nd opinion on this if needed