To determine the minimum amount Darian should expect to contribute for four years at the university, we need to follow several steps to calculate the total annual expenses, account for the grants, and then project these values over four years.
1. Calculate the total annual expenses:
- Tuition: [tex]$18,900
- Room/Board: $[/tex]7,650
- Books/Fees: [tex]$1,475
- Other Expenses: $[/tex]2,350
Total annual expenses:
[tex]\[
18,900 + 7,650 + 1,475 + 2,350 = 30,375
\][/tex]
2. Subtract the annual grants:
- Annual grant: [tex]$7,500
Annual expense after grants:
\[
30,375 - 7,500 = 22,875
\]
3. Calculate the total expenses for four years:
\[
22,875 \times 4 = 91,500
\]
Therefore, the minimum amount Darian should expect to contribute for four years at the university is $[/tex]91,500.
Thus, the answer is:
[tex]\[
\$ 91,500
\][/tex]
