Your client is considering investing in shares from YSN, KRS, and HSN. As their financial advisor, you offer the customer the following three portfolios:

Portfolio A contains three shares of YSN, five of KRS, and eight of HSN.

Portfolio B contains two shares of YSN, three of KRS, and two of HSN.

Portfolio C contains five shares of YSN, two of KRS, and one of HSN.

(a) If your client buys two units of Portfolio A, two units of Portfolio B, and one unit of Portfolio C, how many shares of KRS will they have in total?

(b) Your client wants exactly 27 shares of YSN, 19 shares of KRS, and 16 shares of HSN; they ask you how many units of each portfolio to buy. Set up a linear system which models this question.

You do not need to solve the linear system.

(c) Another client approaches you, and they want to purchase the same portfolios so that they have two shares of YSN, five shares of KRS, and three shares of HSN. They set up a similar linear system the same way you did in part (b), but this time they solve the system themselves and get the solution (x, y, z) = (3, 5, 2).

What can you say to this client?