# Average share price question

I have 6000 shares of stock priced at 1.34/share. I want to how many shares I'll need to purchase at 0.87/share to get an average share price of 1.00/share.

• What have you tried? If you buy $N$ shares at $.87$, what is your average (as a function of $N$)? – lulu Sep 13 '17 at 18:33

Let's talk a little abstractly. You have $S$ shares bought at $P$ dollars each. Then the value of your portfolio is $SP$.
If you buy another $S'$ shares at $P'$ dollars each, the value of those shares would be $S'P'$
A portfolio with an average price per share of $P_A$ is worth $P_AS_T$ where $S_T$ is the total number of shares.
So you want the sum of your two purchases to equal the average portfolio identified, so that $PS+P'S'=P_AS_T$. Finally, you know that $S_T=S+S'$ since $S_T$ is the total number of shares in your portfolio. Do you see how to use the equation $PS+P'S'=P_A(S+S')$ to answer your question?
We want buy $N$ shares such that the average price will be $$\frac{6000\times 1.34+N\times 0.87}{6000+N}=1$$ that is $$6000\times 0.34=N\times 0.13\quad \Longrightarrow\quad N=\frac{6000\times 0.34}{0.13}=15,692$$