SOLUTION: Your friend can buy 20 chairs and two tables for 400 dollars your other friend can buy 8 chairs and 4 tables for 460 dollars. How much will it cost for 12 chairs and 3 tables.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Your friend can buy 20 chairs and two tables for 400 dollars your other friend can buy 8 chairs and 4 tables for 460 dollars. How much will it cost for 12 chairs and 3 tables.      Log On


   



Question 1011214: Your friend can buy 20 chairs and two tables for 400 dollars your other friend can buy 8 chairs and 4 tables for 460 dollars. How much will it cost for 12 chairs and 3 tables.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the cost of 1 chair in dollars
Let +y+ = the cost of 1 table in dollars
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given:
(1) +20x+%2B+2y+=+400+
(2) +8x+%2B+4y+=+460+
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Multiply both sides of (1) by +2+
and subtract (2) from (1)
(1) +40x+%2B+4y+=+800+
(2) +-8x+-+4y+=+-+460+
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+32x+=+340+
+x+=+10.625+
(1) +10x+%2B+y+=+200+
(1) +10%2A10.625+%2B+y+=+200+
(1) +106.25+%2B+y+=200+
(1) +y+=+93.75+
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check:
(2) +2x+%2B+y+=+115+
(2) +2%2A10.625+%2B+93.75+=+115+
(2) +21.25+%2B+93.75+=+115+
and
(1) +10x+%2B+y+=+200+
(1) +10%2A10.625+%2B+93.75+=+200+
(1) +106.25+%2B+93.75+=+200+
(1) +200+=+200+
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+12x+%2B+3y+ = cost of 12 chairs and 3 tables
+12%2A10.625+%2B+3%2A93.75+
+127.5+%2B+281.25+=+408.75+
$408.75 is the cost of 12 chairs and 3 tables