SOLUTION: A grocer mixed 50kilos of first class sugar and third class sugar which he sold at 2.90 a kilo.first class sugar sells at 3.50 a kilo and third class sugar at 2 a kilo. How many ki

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Question 886399: A grocer mixed 50kilos of first class sugar and third class sugar which he sold at 2.90 a kilo.first class sugar sells at 3.50 a kilo and third class sugar at 2 a kilo. How many kilos of first and third class sugar did the grocer mix to produce second class sugar?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = kilos of 1st class sugar needed
Let +b+ = kilos of 3rd class sugar needed
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Given:
(1) +a+%2B+b+=+50+
(2) +%28+3.5a+%2B+2b+%29+%2F+50+=+2.9+
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(2) +3.5a+%2B+2b+=+2.9%2A50+
(2) +3.5a+%2B+2b+=+145+
(2) +35a+%2B+20b+=+1450+
Multiply both sides of (1) by +20+
and subtract (1) from (2)
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(2) +35a+%2B+20b+=+1450+
(1) +-20a+-+20b+=+-1000+
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+15a+=+450+
+a+=+30+
and
(1) +30+%2B+b+=+50+
(1) +b+=+20+
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30 kilos of 1st class sugar are needed
20 kilos of 3rd class sugar are needed
check answer:
(2) +%28+3.5a+%2B+2b+%29+%2F+50+=+2.9+
(2) +%28+3.5%2A30+%2B+2%2A20+%29+%2F+50+=+2.9+
(2) +%28+105+%2B+40+%29+%2F+50+=+2.9+
(2) +145+=+2.9%2A50+
(2) +145+=+145+
OK