Question

financial literacy
short quiz2
solve the following items by applying your knowledge of scholarships, financial aid, and tuition costs. for each problem:
-identify the type of scholarship/aid (merit-based or need-based).
-write the tuition function as:
net tuition cost=total tuition-(merit scholarships+need-based aid)
-substitute the given values into the function.
-compute the net tuition cost the student will pay out-of-pocket
for case studies, carefully read the scenario and:
-determine which scholarships are merit-based and which are need-based.
-apply the net tuition function to calculate the final cost.
-provide a short explanation of your reasoning.

1. miguel has a 4.0 gpa and scored in the top 5% on her sat exam. she applies for a scholarship that rewards students for academic excellence.
2. john’s family income is below the state poverty line. he qualifies for financial aid that covers tuition and books.
3. evelyn is a talented violinist who won several state-level competitions. she receives a scholarship from a music foundation.
4. marcus comes from a low-income household and applies for assistance through the fafsa, which helps determine eligibility for state and federal grants.
5. matthea is the captain of her high school basketball team and is offered a full scholarship to play for a university team.

Explanation:

1. Miguel's Case

Step1: Identify Scholarship Type

Miguel's scholarship is for academic excellence (top 5% in SAT, 4.0 GPA), so it's Merit - Based.

Step2: Define Net Tuition Function

Net Tuition Cost = Total Tuition - Merit - Based Scholarship (let's assume Total Tuition is \( T \) and Scholarship is \( S \), so \( \text{Net Cost}=T - S \)). But since no numerical values for \( T \) and \( S \) are given, we note that the net cost is total tuition minus the merit - based scholarship amount.

Step1: Identify Aid Type

John's family income is below the poverty line, and the aid covers tuition and books. This is Need - Based as it's based on financial need.

Step2: Define Net Tuition Function

Net Tuition Cost = Total Tuition - Need - Based Aid (let Total Tuition be \( T \) and Need - Based Aid be \( A \), so \( \text{Net Cost}=T - A \)). Without numerical values for \( T \) and \( A \), we state the function.

Step1: Identify Scholarship Type

Evelyn won a scholarship for her musical talent (won state - level competitions), so it's Merit - Based.

Step2: Define Net Tuition Function

Net Tuition Cost = Total Tuition - Merit - Based Scholarship (let Total Tuition be \( T \) and Scholarship be \( S \), so \( \text{Net Cost}=T - S \)). Without numerical values for \( T \) and \( S \), we state the function.

Answer:

Scholarship Type: Merit - Based. Net Tuition Function: \( \text{Net Tuition Cost}=\text{Total Tuition}-\text{Merit - Based Scholarship} \). (Numerical calculation not possible without \( T \) and \( S \) values)

2. John's Case