Answer:
Let +a+ = gallons of 55% antifreeze needed
Let +b+ = gallons of 95% antifreeze needed
-----------------------
(1) +a+%2B+b+=+160+
(2) +%28+.55a+%2B+.95b+%29+%2F+160+=+.85+
-----------------------------------
(2) +.55a+%2B+.95b+=+.85%2A160+
(2) +.55a+%2B+.95b+=+136+
(2) +55a+%2B+95b+=+13600+
(2) +11a+%2B+19b+=+2720+
----------------------------
Multiply both sides of (1) by +11+
and subtract (1) from (2)
(2) +11a+%2B+19b+=+2720+
(1) +-11a+-+11b+=+-1760+
---------------------------
+8b+=+960+
+b+=+120+
and
(1) +a+%2B+120+=+160+
(1) +a+=+40+
-------------------
40 gallons of 55% antifreeze are needed
120 gallons of 95% antifreeze are needed
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check:
(2) +%28+.55a+%2B+.95b+%29+%2F+160+=+.85+
(2) +%28+.55%2A40+%2B+.95%2A120+%29+%2F+160+=+.85+
(2) +%28+22+%2B+114+%29+%2F+160+=+.85+
(2) +136+=+.85%2A160+
(2) +136+=+136+
OK
Step-by-step explanation:
