SOLUTION: A student bought 3 boxes of pencils and 2 boxes of pens for $6. He then bought 2 boxes of pencils and 4 boxes of pens for $8. Find the cost of each box of pencils and pens.

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Question 1013311: A student bought 3 boxes of pencils and 2 boxes of pens for $6. He then bought 2 boxes of pencils and 4 boxes of pens for $8. Find the cost of each box of pencils and pens.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost of a box of pencils
Let +b+ = the cost of a box of pens
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(1) +3a+%2B+2b+=+6+
(2) +2a+%2B+4b+=+8+
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Multiply both sides of (1) by +2+
and subtract (2) from (1)
(1) +6a+%2B+4b+=+12+
(2) +-2a+-+4b+=+-8+
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+4a+=+4+
+a+=+1+
and
(1) +3a+%2B+2b+=+6+
(1) +3%2A1+%2B+2b+=+6+
(1) +3+%2B+2b+=+6+
(1) +2b+=+3+
(1) +b+=+1.5+
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A box of pencils costs $1
A box of pens costs $1.50
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check:
(2) +2a+%2B+4b+=+8+
(2) +a+%2B+2b+=+4+
(2) +1+%2B+2%2A1.5+=+4+
(2) +1+%2B+3+=+4+
(2) +4+=+4+
OK