SOLUTION: A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 160 gallons of a mixture

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 160 gallons of a mixture       Log On


   



Question 1149424: A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 160 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of the 35% antifreeze needed
Let +b+ = gallons of the 60% antifreeze needed
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(1) +a+%2B+b+=+160+
(2) +%28+.35a+%2B+.6b+%29+%2F+160+=+.45+
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(2) +.35a+%2B+.6b+=+72+
(2) +35a+%2B+60b+=+7200+
(2) +7a+%2B+12b+=+1440+
Multiply both sides of (1) by +7+ and
subtract (1) from (2)
(2) +7a+%2B+12b+=+1440+
(1) +-7a+-+7b+=+-1120+
------------------------------
+5b+=+320+
+b+=+64+
and
(1) +a+%2B+64+=+160+
(1) +a+=+96++
--------------------------
96 gallons of the 35% antifreeze are needed
64 gallons of the 60% antifreeze are needed
--------------------------
check:
(2) +%28+.35a+%2B+.6b+%29+%2F+160+=+.45+
(2) +%28+.35%2A96+%2B+.6%2A64+%29+%2F+160+=+.45+
(2) +%28+33.6+%2B+38.4+%29+%2F+160+=+.45+
(2) +72+%2F+160+=+.45+
(2) +.45+=+.45+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Mix the two in a ratio determined by where the 45% lies between 35% and 60%.

35 to 45 is 10; 35 to 60 is 25. 45 is 10/25 = 2/5 of the way from 35 to 60.

That means 2/5 of the mixture needs to be the 60% antifreeze.

ANSWER: 2/5 of 160 gallons, or 64 gallons, of the 60% antifreeze; 3/5 of the 160 gallons, or 96 gallons, of the 35% antifreeze.