SOLUTION: i buy 20 pencils at a certain price and 30 other more expensive pencils.the pencils cost me 90p.had i bought 30 of the cheaper pencils and the 20 of the dearer , i should have save

Algebra ->  Linear-equations -> SOLUTION: i buy 20 pencils at a certain price and 30 other more expensive pencils.the pencils cost me 90p.had i bought 30 of the cheaper pencils and the 20 of the dearer , i should have save      Log On


   



Question 616419: i buy 20 pencils at a certain price and 30 other more expensive pencils.the pencils cost me 90p.had i bought 30 of the cheaper pencils and the 20 of the dearer , i should have saved 5p.find the cost of of one of the dearer pencils.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = price of one of the cheaper pencils
Let +b+ = price of one of the dearer pencils
given:
+20a+%2B+30b+=+90+
(1) +2a+%2B+3b+=+9+
and
+30a+%2B+20b+=+90+-+5+
+30a+%2B+20b+=+85+
(2) +6a+%2B+4b+=+17+
Multiply both sides of (1) by +3+
and subtract (2) from (1)
(1) +6a+%2B+9b+=+27+
(2) +-6a+-+4b+=+-17+
+5b+=+10+
+b+=+2+
and, since
(1) +2a+%2B+3b+=+9+
(1) +2a+%2B+3%2A2+=+9+
(1) +2a+=+9+-+6+
(1) +2a+=+3+
(1) +a+=+1.5+
1.5p is the price of one of the cheaper pencils
2p is the price of one of the dearer pencils
check:
(2) +6a+%2B+4b+=+17+
(2) +6%2A1.5+%2B+4%2A2+=+17+
(2) +9+%2B+8+=+17+
(2) +17+=+17+
You can check (1)