SOLUTION: carl manages a highway department garage in maine. a mixture of salt and sand is stored in the garage for use during the winter. carl needs 24 tons of a salt/sand mixture that is 2

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Question 732980: carl manages a highway department garage in maine. a mixture of salt and sand is stored in the garage for use during the winter. carl needs 24 tons of a salt/sand mixture that is 25% salt. he will combine shipments of 15% salt and shipments of 30% salt to achieve the desired 24 tons. how much of each type should he use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = tons of 15% salt needed
Let +b+ = tons of 30% salt needed
given:
(1) +a+%2B+b+=+24+
(2) +%28+.15a+%2B+.3b+%29+%2F+24+=+.25+
----------------------------
(2) +.15a+%2B+.3b+=+.25%2A24+
(2) +.15a+%2B+.3b+=+6+
(2) +15a+%2B+30b+=+600+
Multiply both sides of (1) by +15+
and subtract (1) from (2)
---------------------
(2) +15a+%2B+30b+=+600+
(1) +-15a+-+15b+=+-360+
+15b+=+240+
+b+=+16+
and, since
(1) +a+%2B+b+=+24+
(1) +a+=+8+
8 tons of 15% salt are needed
16 tons of 30% salt are needed
check:
(2) +%28+.15a+%2B+.3b+%29+%2F+24+=+.25+
(2) +%28+.15%2A8+%2B+.3%2A16+%29+%2F+24+=+.25+
(2) +%28+1.2+%2B+4.8+%29+%2F+24+=+.25+
(2) +6%2F24+=+.25+
(2) +6+=+.25%2A24+
(2) +6+=+6+
OK