Problem
Each time Trisha went to the school cafeteria, she either paid $\$ 1.75$ for a bowl of soup or she spent $\$ 4.75$ on a main course. During the school year, she spent $\$ 490$ in total and she bought 160 items of food. Set up the system of equations that can be used to solve this question. Be sure to write "Let statements", and complete equations. Do Not Solve.
Solution
Step 1 ：Let x = the number of bowls of soup
Step 2 ：Let y = the number of main courses
Step 3 ：\(1.75x + 4.75y = 490\) (total amount spent)
Step 4 ：\(x + y = 160\) (total number of items)
Step 5 ：\(\boxed{\begin{cases} 1.75x + 4.75y = 490 \\ x + y = 160 \end{cases}}\)
