Consider a database schema with the following tables:

CREATE TABLE Students $($

StudentID INT PRIMARY KEY,

Name VARCHAR$(50),$

Age INT,

GPA FLOAT $)$;

CREATE TABLE Courses $($

CourseID INT PRIMARY KEY,

CourseName VARCHAR$(50))$;

CREATE TABLE Enrollments $($

EnrollmentID INT PRIMARY KEY,

StudentID INT,

CourseID INT,

Grade FLOAT,

FOREIGN KEY $($StudentID$)$ REFERENCES Students$($StudentID$),$

FOREIGN KEY $($CourseID$)$ REFERENCES Courses$($CourselD$))$;

Solve the following SQL problems by nesting queries.

Write an $SQL$ query to find the names of students who are enrolled in the

course 'Mathematics' and have a GPA greater than $3\mathrm{.}5.$

Assuming the same database schema, write an $SQL$ query to find the average

GPA of students who have enrolled in the course 'Physics'.

Extend the previous query to find the average GPA of students who have

enrolled in the course 'Physics' and whose age is less than $25.$