SOLUTION: Mary had bought 20 bowls and plates for $96. If each bowl cost $4.50 each and the plate cost $1.50 more than the bowl. Mary had more bowls than plates.how many bowls and plates did

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Mary had bought 20 bowls and plates for $96. If each bowl cost $4.50 each and the plate cost $1.50 more than the bowl. Mary had more bowls than plates.how many bowls and plates did      Log On


   

Question 916512: Mary had bought 20 bowls and plates for $96. If each bowl cost $4.50 each and the plate cost $1.50 more than the bowl. Mary had more bowls than plates.how many bowls and plates did Mary have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of bowls
Let +b+ = number of plates
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(1) +a+%2B+b+=+20+
(2) +4.5a+%2B+6b+=+96+
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(2) +45a+%2B+60b+=+960+
(2) +9a+%2B+12b+=+192+
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Multiply both sides of (1) by +9+
and subtract (1) from (2)
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(2) +9a+%2B+12b+=+192+
(1) +-9a+-+9b+=+-180+
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+3b+=+12+
+b+=+4+
and, since
(1) +a+%2B+b+=+20+
(1) +a+=+16+
She has 16 bowls and 4 plates
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check:
(2) +4.5%2A16+%2B+6%2A4+=+96+
(2) +72+%2B+24+=+96+
(2) +96+=+96+
OK