SOLUTION: Find how many quarts of 6% butterfat milk and 3 % butterfat milk should be mixed to yield 45 quarts of 5% butterfat milk

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Question 412152: Find how many quarts of 6% butterfat milk and 3 % butterfat milk should be mixed to yield 45 quarts of 5% butterfat milk
Found 2 solutions by emargo19, josmiceli:
Answer by emargo19(101) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= number of quarts of 6% buttermilk
y= number of quarts of 3% buttermilk
____________
EQ 1
------------
x%2By=45
Multiply 0.03 by EQ (1)
---------
0.03%2Ax%2B0.03%2Ay=45%280.03%29
0.03x%2B0.03y=1.35
__________
EQ 2
----------
0.06x%2B0.03y=0.05%2845%29 ----(Simplfy this EQ 2)
0.06x%2B0.03y=2.25
Therefore
0.03x%2B0.03y=1.35 (Eq 1)
0.06x%2B0.03y=2.25 (Eq 2)
Subtract (Eq 1) from (Eq 2)
++++0.03y=0.90
+++++y=+30
x%2B30=45
x=15
15 quarts of 6% buttermilk are mixed with 15 quarts of 3% buttermilk.






Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = quarts of 6% milk needed
Let b = quarts of 3% milk needed
------------------------------
In words:
(total quarts of butterfat)/(total quarts of milk) = 5%
(1) %28.06a+%2B+.03b%29%2F%28a+%2B+b%29+=+.05
(2) a+%2B+b+=+45
---------------
From (1)
(1) .06a+%2B+.03b+=+.05%2A%28a+%2B+b%29
(1) .06a+%2B+.03b+=+.05a+%2B+.05b
(1) .01a+=+.02b
(1) a+=+2b
----------------
(2) 2b+%2B+b+=+45
(2) 3b+=+45
(2) b+=+15
and,
(2) a+=+45+-+15
(2) a+=+30
30 quarts of 6% and 15 quarts of 3% butterfat milk are needed
check answer:
(1) .06a+%2B+.03b+=+.05%2A%28a+%2B+b%29
(1) .06%2A30+%2B+.03%2A15+=+.05%2A45
(1) 1.8+%2B+.45+=+2.25
(1) 2.25+=+2.25
OK