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, wish to hold $\frac{4}{10}$ 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 technoog$)$

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 gien situaion.

Ifyou simply write down a solution without setting up a system of equations you get zero credit.

$[$Note that fractions of shares are possible, and in fact quite common in actual stock market transactions; in some cases some shares are so expensive that people sometimes purchase only a fraction of a share. For instance, a single share of Berkshire Hathaway costs around $$6800($as of Match $2024).$

Note: Following the method required will result in fractions and not decimals, as $($rounded$)$decimals are seldom exact. $($Text in picture$)$