SOLUTION: Solve this application problem using a system of equations: The owner of Jeremy’s Garage wants to fill a 55-gallon drum with a 20% winter mixture of antifreeze for is customers.

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Question 1157655: Solve this application problem using a system of equations: The owner of Jeremy’s Garage
wants to fill a 55-gallon drum with a 20% winter mixture of antifreeze for is customers. How
many gallons of 100% antifreeze should he mix with some 12% antifreeze mixture in order to
fill the drum?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = gallons of 100% antifreeze needed
Let +y+ = gallons of 12% antifreeze needed
-----------------------------------------------------
The amount of pure antifreeze the owner ends up with will be:
+.2%2A55+=+11+ gallons
+1%2Ax+%2B+.12y+ is also the amount of pure antifreeze owner
ends up with
-----------------------
(1) +x+%2B+y+=+55+
(2) +x+%2B+.12y+=+.2%2A55+
----------------------------------
(2) +x+%2B+.12y+=+11+
(2) +100x+%2B+12y+=+1100+
(2) +25x+%2B+3y+=+275+
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +25x+%2B+3y+=+275+
(1) +-3x+-+3y+=+-165+
----------------------------
+22x+=+110+
+x+=+5+
and
(1) +x+%2B+y+=+55+
(1) +5+%2B+y+=+55+
(1) +y+=+50+
-------------------------------
5 gallons of 100% antifreeze are needed
-------------------------------
check:
(2) +x+%2B+.12y+=+.2%2A55+
(2) +5+%2B+.12%2A50+=+.2%2A55+
(2) +5+%2B+6+=+11+
(2) +11+=+11+
OK