SOLUTION: Sarah Myers has $31,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $80 a share. If stock B triples in value and stock A goes up

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Sarah Myers has $31,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $80 a share. If stock B triples in value and stock A goes up       Log On

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Question 1093936: Sarah Myers has $31,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $80 a share. If stock B triples in value and stock A goes up 50%, her stock will be worth $70,500. How many shares of each stock does she own?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of shares of stock A
Let +b+ = number of shares of stock B
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(1) +50a+%2B+80b+=+31000+
(2) +1.5%2A50a+%2B+3%2A80b+=+70500+
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(2) +75a+%2B+240b+=+70500+
(2) +15a+%2B+48b+=+14100+
(2) +5a+%2B+16b+=+4700+
and
(1) +5a+%2B+8b+=+3100+
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Subtract (1) from (2)
(2) +5a+%2B+16b+=+4700+
(1) +-5a+-+8b+=+-3100+
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+8b+=+1600+
+b+=+200+
and
(1) +5a+%2B+8b+=+3100+
(1) +5a+%2B+8%2A200+=+3100+
(1) +5a+=+3100+-+1600+
(1) +5a+=+1500+
(1) +a+=+300+
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She owns 300 shares of stock A
She owns 200 shares of stock B
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check:
(2) +5a+%2B+16b+=+4700+
(2) +5%2A300+%2B+16%2A200+=+4700+
(2) +1500+%2B+3200+=+4700+
(2) +4700+=+4700+
OK