Evaluate Algebraic Expressions

An algebraic expression uses variables and numbers to represent a quantity that changes with variable values. To evaluate it, substitute given values and simplify using the order of operations.

Imagine Noah, a college student who works as a freelance tutor to help pay for his education. He charges 12 dollars per hour for math tutoring and 8 dollars per hour for exam-preparation sessions.

He represents his weekly earnings with an algebraic expression in which x is the number of math tutoring hours, and y is the number of exam-preparation hours.

During the first week of the semester, Noah tutors for 5 hours in math and 4 hours in exam preparation.

Substituting the values of x and y into the expression and evaluating it gives 92 dollars, which is his earnings for that week.

A few weeks later, during midterm exams, the demand for tutoring increases. That week, Noah tutors for 8 hours in math and 10 hours in exam preparation.

Substituting the values of x and y into the same expression and evaluating it gives 176 dollars, which is his earnings for that week.

Using this expression, Noah can quickly calculate how much he earns each week.