SOLUTION: Two types of books (A and B) are to be placed on a library shelf of 96 cm length, with a maximum load of 20 kg. If the weight of each type of the books is 1 kg, and the thickness o

Algebra ->  Graphs -> SOLUTION: Two types of books (A and B) are to be placed on a library shelf of 96 cm length, with a maximum load of 20 kg. If the weight of each type of the books is 1 kg, and the thickness o      Log On


   

Question 1127969: Two types of books (A and B) are to be placed on a library shelf of 96 cm length, with a maximum load of 20 kg. If the weight of each type of the books is 1 kg, and the thickness of type A is 6 cm whereas the thickness of type B is 4 cm, What is the number of books of each type that should be placed on the shelf so that the number of books is maximized?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +6a+%2B+4b+=+96+
(2) +a+%2B+b+%3C=+20+
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I'll use the maximum for (2)
and subtract (2) from (1)
(1) +3a+%2B+2b+=+48+
(2) +-2a+-+2b+=+-40+
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+a+=+8+
and
+a+%2B+b+=+20+
+8+%2B+b+=+20+
+b+=+12+
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8 of type A and 12 of type B
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check:
what if there are 9 of A and 11 of B?
(1) +3a+%2B+2b+=+48+
(1) +3%2A9+%2B+2%2A11+=+48+
(1) +27+%2B+22+=+49+
doesn't work
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what if there are 7 of A and 13 of B?
(1) +3%2A7+%2B+2%2A13+=+48+
(1) +21+%2B+26+=+47+
doesn't work
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What if there are 10 of A and 10 of B?
+3%2A10+%2B+2%2A10+=+48+
+30+%2B+20+=+50+ doesn't work
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Looks like my answer is correct