SOLUTION: how much 1% milk and how much 4% milk must be combined to obtain 60 liters of 2% milk

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: how much 1% milk and how much 4% milk must be combined to obtain 60 liters of 2% milk      Log On


   



Question 777738: how much 1% milk and how much 4% milk must be combined to obtain 60 liters of 2% milk
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 1% milk needed
Let +b+ = liters of 4% milk needed
+.01a+ = liters of fat in 1% milk
+.04b+ = liters of fat in 4% milk
------------------------------
(1) +a+%2B+b+=+60+
(2) +%28+.01a+%2B+.04b+%29+%2F+60+=+.02+
-----------------------------
(2) +.01a+%2B+.04b+=+.02%2A60+
(2) +.01a+%2B+.04b+=+1.2+
(2) +a+%2B+4b+=+120+
-------------------
Subtract (1) from (2)
(2) +a+%2B+4b+=+120+
(1) +-a+-+b+=+-60+
+3b+=+60+
+b+=+20+
and, since
(1) +a+%2B+b+=+60+
(1) +a+=+60+-+20+
(1) +a=+40+
-------------
40 liters of 1% milk are needed
20 liters of 4% milk are needed
check:
(2) +%28+.01a+%2B+.04b+%29+%2F+60+=+.02+
(2) +%28+.01%2A40+%2B+.04%2A20+%29+%2F+60+=+.02+
(2) +%28+.4+%2B+.8+%29+%2F+60+=+.02+
(2) +1.2+=+.02%2A60+
(2) +1.2+=+1.2+
OK