SOLUTION: The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 75% pure fruit juice. The company is attempting t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 75% pure fruit juice. The company is attempting t      Log On


   



Question 991103: The Royal Fruit Company produces two types of fruit drinks. The first type is
35%
pure fruit juice, and the second type is
75%
pure fruit juice. The company is attempting to produce a fruit drink that contains
60%
pure fruit juice. How many pints of each of the two existing types of drink must be used to make
40
pints of a mixture that is
60%
pure fruit juice?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a = pints of the 35% mixture needed
Let +b+ = pints of the 75% mixture needed
----------------
(1) +a+%2B+b+=+40+
(2) +%28+.35a+%2B+.75b+%29+%2F+40+=+.6+
---------------------------
(2) +.35a+%2B+.75b+=+.6%2A40+
(2) +35a+%2B+75b+=+2400+
Multiply both sides of (1) by +35+
and subtract (1) from (2)
(2) +35a+%2B+75b+=+2400+
(1) +-35a+-+35b+=+-1400+
------------------------
+40b+=+1000+
+b+=+25+
and
(1) +a+%2B+b+=+40+
(1) +a+=+15+
-----------------
15 pints of the 35% mixture are needed
25 pints of the 75% mixture are needed
----------------
check:
(2) +%28+.35a+%2B+.75b+%29+%2F+40+=+.6+
(2) +%28+.35%2A15+%2B+.75%2A25+%29+%2F+40+=+.6+
You can finish this check