Question 166079
I am sorry, but I think something is missing in this problem ...at least the way it is written.  The cost of the booth is a fixed cost of $312 dollars that vendors must spend in order to operate at a fair and $1410 is a fixed amount that the vendor would like to earn.   We can only really generate one equation here with 2 variables as far as I can see

 and that would be if A were the number of small milkshakes
 ............     and B were the number of large milkshakes

then (2.25-.45)A + (3.00-.75)B = $1410+312 (amount you want to make plus fixed costs)   so 1.80A+2.25B=1522.   

we need more information to solve this in my opinion.

SO MAYBE YOUR TEACHER IS CRAZY EITHER THAT OR I AM....LOL