To determine the minimum amount Darian should expect to contribute for four years at the university, let's follow these steps:
1. Calculate the Total Annual Expenses:
Darian's expected annual expenses are:
- Tuition: [tex]$18,900
- Room/Board: $[/tex]7,650
- Books/Fees: [tex]$1,475
- Other Expenses: $[/tex]2,350
Adding these together:
[tex]\[
18,900 \, (\text{tuition}) + 7,650 \, (\text{room/board}) + 1,475 \, (\text{books/fees}) + 2,350 \, (\text{other expenses}) = 30,375
\][/tex]
Therefore, Darian's total annual expenses amount to [tex]$30,375.
2. Calculate the Annual Contribution After Grants:
Darian expects to receive $[/tex]7,500 in grants each year. To find the amount he needs to contribute annually after grants:
[tex]\[
30,375 \, (\text{total annual expenses}) - 7,500 \, (\text{annual grants}) = 22,875
\][/tex]
So, Darian's annual contribution after grants is [tex]$22,875.
3. Calculate the Total Contribution for Four Years:
To find the total contribution for four years, multiply the annual contribution by 4:
\[
22,875 \, (\text{annual contribution}) \times 4 \, (\text{years}) = 91,500
\]
Thus, over four years, Darian should expect to contribute a total of $[/tex]91,500.
Therefore, the minimum amount Darian should expect to contribute for four years at the university is [tex]$91,500. Hence, the correct answer is $[/tex]\[tex]$ 91,500$[/tex].
