An online bookstore sells novels and magazines. Each novel...

An online bookstore sells novels and magazines. Each novel sells for $\$ 4,$ and each magazine sells for $\$ 1 .$ If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $\$ 20,$ how many novels did she purchase? $$\begin{array}{l}{\text { A) } 2} \\ {\text { B) } 3} \\ {\text { C) } 4} \\ {\text { D) } 5}\end{array} $$

An online bookstore sells novels and magazines.
Each novel sells for $\$ 4,$ and each magazine sells for
$\$ 1 .$ If Sadie purchased a total of 11 novels and
magazines that have a combined selling price of $\$ 20,$
how many novels did she purchase?
$$\begin{array}{l}{\text { A) } 2} \\ {\text { B) } 3} \\ {\text { C) } 4} \\ {\text { D) } 5}\end{array}
$$

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Key Concepts

Integer Solutions in Linear Equations

In many real-world problems, particularly those dealing with counts or items, the solutions to the equations must be whole numbers. Recognizing that the variables represent quantities that cannot be fractional is essential. This property can sometimes narrow the possible solutions or provide a check on the final answer.

Substitution Method

Often used to solve a system of equations, the substitution method involves isolating one variable in one equation and then substituting that expression into another equation. This technique simplifies the problem by reducing it to a single equation with one unknown, which can then be solved step by step.

System of Linear Equations

This concept involves representing a word problem with multiple unknowns using two or more mathematical equations that are simultaneously true. In many real-world scenarios, such as determining quantities based on total amounts and costs, a system of linear equations allows one to capture all given conditions in the form of algebraic expressions and then solve for the unknown variables.

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