To determine how much Sophie will need to pay each year from her own savings and from loans, let's break down the cost and the financial aid components step by step.
### Step 1: Calculate Total Costs
1. Tuition & Fees: [tex]\(\$ 11,750\)[/tex]
2. Room & Board: [tex]\(\$ 11,500\)[/tex]
To get the total costs, add the Tuition & Fees to the Room & Board:
[tex]\[
\text{Total Costs} = \$ 11,750 + \$ 11,500 = \$ 23,250
\][/tex]
### Step 2: Calculate Total Financial Aid
1. Grants & Scholarships: [tex]\(\$ 9,000\)[/tex]
2. Work-Study: [tex]\(\$ 7,000\)[/tex]
3. Parents' Contribution: [tex]\(\$ 3,500\)[/tex]
To get the total aid package, add together the Grants & Scholarships, Work-Study, and Parents' Contribution:
[tex]\[
\text{Total Aid} = \$ 9,000 + \$ 7,000 + \$ 3,500 = \$ 19,500
\][/tex]
### Step 3: Calculate the Amount Sophie Needs to Pay
To find out how much Sophie will need to pay from her own savings and loans, subtract the total financial aid from the total costs:
[tex]\[
\text{Amount Needed} = \text{Total Costs} - \text{Total Aid}
\][/tex]
Substitute the values we have:
[tex]\[
\text{Amount Needed} = \$ 23,250 - \$ 19,500 = \$ 3,750
\][/tex]
Thus, Sophie will need to pay \[tex]$ 3,750 each year from her own savings and from loans.
The correct answer is:
\[
\$[/tex] 3,750
\]
