Your portfolio manager has suggested the following two companies or investment purposes: Alpha Centauri and Beta Bank. Alpha Centauri shares cost $$40$ per share, while Beta Bank shares cost $$22$ per share. You have $$16,950$ to invest and wish to hold $75\%$ the number of Beta Bank shares as Alpha Centauri shares. How many shares of each company should you buy? $[$Hint: See Example $6$ of Section $3\mathrm{.}1]$

The local sushi bar serves $2-$ounce pieces of raw whitefish $($consisting of $10\%$ protein$)$ and $4-$ounce pieces of raw shrimp $(5\%$ protein$).$ A customer's total intake of protein amounts to $1$ ounce after consuming a total of five pieces. How many of each type did the customer consume? $($Fractions of pieces are permitted.$)$

$($Please do all questions with step by step$)$