Your portfolio manager has suggested the following three companies for investment purposes: Epsilon NanoTech, Zeta Functions, and Delta Derivatives. Epsilon NanoTech shares cost $28 per share, Zeta Functions shares cost $12 per share, and Delta Derivatives shares cost $12 per share. You have $2,532 to invest and wish to hold 4/10 the number of Zeta Functions shares as Delta Derivatives shares, and (for reasons too complicated to explain) a total of 179 shares. How many shares of each company should you buy?
Use the given information to set up a system of linear equations in two unknowns
Solve that system by any method (including technology)
If the given information leads to a system of equations with infinitely many solutions, you must state the general solution and interpret it in the context of the given situation.