SOLUTION: A furniture shop refinishes tables. Employees use one of two methods to refinish each table. Method I takes 0.5 hours and the material costs $8. Method II takes 1.5 hours, and t

Algebra ->  Square-cubic-other-roots -> SOLUTION: A furniture shop refinishes tables. Employees use one of two methods to refinish each table. Method I takes 0.5 hours and the material costs $8. Method II takes 1.5 hours, and t      Log On


   

Question 1030286: A furniture shop refinishes tables. Employees use one of two methods to refinish each table. Method I takes 0.5 hours and the material costs $8. Method II takes 1.5 hours, and the material costs $5. Next week, they plan to spend 92 hours in labor and $484 in material for refinishing tables. How many tables should they plan to refinish with each method?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of tables refinished using method 1
Let +b+ = number of tables refinished using method 2
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(1) +.5a+%2B+1.5b+=+92+
(2) +8a+%2B+5b+=+484+
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(1) +5a+%2B+15b+=+920+
(1) +a+%2B+3b+=+184+
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Multiply both sides of (1) by +8+
and subtract (2) from (1)
(1) +8a+%2B+24b+=+1472+
(2) +-8a+-+5b+=+-484+
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+19b+=+988+
+b+=+52+
and
(1) +a+%2B+3b+=+184+
(1) +a+%2B+3%2A52+=+184+
(1) +a+%2B+156+=+184+
(1) +a+=+28+
They should refinish 28 tables using method 1
They should refinish 52 tables using method 2
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(1) +.5a+%2B+1.5b+=+92+
(1) +.5%2A28+%2B+1.5%2A52+=+92+
(1) +14+%2B+78+=+92+
(1) +92+=+92+
OK
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