A dietician in a hospital has to arrange a special diet composed of three basic foods: food A$,$ food B$,$ and food C$.$ The diet is to include exactly $110$ units of calcium, $138$ units of iron, and $496$ units of vitamin A$.$ A breakdown of the nutritional information per ounce in each food is given by the following table:

$\backslash$table$[[,$Food A$,$Food B$,$Food C$],[$Calcium$,1,5,7],[$Iron$,1,6,9],[$Vitamin A$,4,22,32]]$

Let $x_1$ be the number of ounces of food A$,x_2$ the number of ounces of food $B,$ and $x_3$ the number of ounces of food C$.$ Write a system of equations involving $x_1,x_2,$ and $x_3,$ solve the system, and give the answers in the boxes below. If the system is dependent, write expressions for the answers in terms of $t.$

$x_1=$

$x_2=$

$x_3=$

If the system is dependent, list the plausible values of $t($separate your answers with commas$).$ If the svstem is not debendent. leave the answer boxes in this section blank.

List the corresponding blausible values of $x_1.$

List the corresponding plausible values of $x_2.$

List the corresponding plausible values of $x_3.$