Shanika has invested three different stocks . stock a is currently worth $5.50 per share. stock b is worth $9.00 per share, while stock c is worth $10.00 per share. shanika purchased half as many shares of stock b as stock a and half as many shares of stock c as stock b. if her total investments are currently worth $850 how many shares of each stock does she own?

Let a, b, c represent the number of shares of A, B, and C that Shanika owns.
.. 5.50a +9.00b +10.00c = 850 . . . . . . the current value of Shanika's investment
.. b = a/2 . . . . . . . . . . . . . . . . . . . . . . . . . half as many shares of B as of A
.. c = b/2 . . . . . . . . . . . . . . . . . . . . . . . . . half as many shares of C as of B

Substituting, we have
.. 5.50a +9.00(a/2) +10.00(a/4) = 850
.. a = 850/(5.50 +4.50 +2.50) = 68
.. b = 68/2 = 34
.. c = 34/2 = 17

Shanika owns
  68 shares of A
  34 shares of B
  17 shares of C