SOLUTION: Ed bought $2,000 in stock shares one week before the stock price dropped $10.00. If he had waited for the price setback, he could have bought 10 more shares for the same amount. Ho

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Ed bought $2,000 in stock shares one week before the stock price dropped $10.00. If he had waited for the price setback, he could have bought 10 more shares for the same amount. Ho      Log On


   

Question 621264: Ed bought $2,000 in stock shares one week before the stock price dropped $10.00. If he had waited for the price setback, he could have bought 10 more shares for the same amount. How many shares did he buy?
40, 50, or 60?
Found 2 solutions by josmiceli, Emsley:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = the price/share before the price dropped
Let +n+ = the number of shares he actually bought
given:
(1) +2000+=+n%2Ap+
(2) +2000+=+%28+n+%2B+10+%29%2A%28+p+-+10+%29+
---------------------------
(1) +p+=+2000%2Fn+
Substitute this into (2)
(2) +2000+=+%28+n+%2B+10+%29%2A%28+2000%2Fn+-+10+%29+
(2) +2000+=+2000+%2B+20000%2Fn+-+10n+-+100+
(2) +20000%2Fn+=+10n+%2B+100+
Multiply both sides by +n+
(2) +20000+=+10n%5E2+%2B+100n+
(2) +10n%5E2+%2B+100n+-+20000+=+0+
(2) +n%5E2+%2B+10n+-+2000+=+0+
Use quadratic formula
+n+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+10+
+c+=+-2000+
+n+=+%28+-10+%2B-+sqrt%28+10%5E2+-+4%2A1%2A%28-2000%29+%29%29+%2F+%282%2A1%29+
+n+=+%28+-10+%2B-+sqrt%28+100+%2B+8000+%29%29+%2F+2+
+n+=+%28+-10+%2B-+sqrt%28+8100+%29%29+%2F+2+
+n+=+%28+-10+%2B+90%29+%2F+2+ ( can't use the negative square root )
+n+=+80%2F2+
+n+=+40+
He bought 40 shares
check answer:
(1) +2000+=+40p+
(1) +p+=+50+
and
(2) +2000+=+%28+40+%2B+10+%29%2A%28+p+-+10+%29+
(2) +2000+=+50p+-+500+
(2) +50p+=+2500+
(2) +p+=+50+
OK

Answer by Emsley(35) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=original price SO number bought=2000/x
New price=x-10 So number bought= 2000/X-10) This is 10 more than before
So 2000/(x-10)-2000/x =10
Muliply throughout by x(x-10)getting 2000x-2000(x-10)= 10x(x-10)
Divide throughout by and rearrange x^2-10x-2000=0 (x-50)(x+40)=0 So x=50
That is original price was 50 So number bought was 2000/50=40