Eight students in Ms. Reese's class decided to purchase...

Eight students in Ms. Reese's class decided to purchase their textbooks from two different sources. Some students purchased the textbook from the college bookstore for $\$ 95.50 .$ The other students purchased the textbook from an online discount store for $\$ 65$ per book. If the total amount spent by the eight students is $\$ 611.50,$ how many students purchased the book online?

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Key Concepts

Variable Definition

This concept involves representing unknown quantities with symbols, typically letters, to simplify the modeling of real-world situations. By defining variables, we can create algebraic expressions that make it easier to set up and solve equations derived from a problem statement.

Translating Word Problems into Equations

Translating word problems into equations is a key step in problem-solving where the information given in a narrative is converted into mathematical expressions. This process involves identifying the relevant quantities, their relationships, and representing them through algebraic equations.

Linear Equations

Linear equations are algebraic expressions that equate to a constant and involve only first-degree terms (variables raised to the power of one). They provide a straightforward method for modeling relationships and solving for unknown values in many real-world applications.

Algebraic Manipulation

Algebraic manipulation refers to the use of operations such as addition, subtraction, multiplication, division, and the distributive property to rearrange and simplify equations. This process is essential for isolating variables and finding their values in linear equations.

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