Compact Discs. A music store has compact discs on sale for...

Compact Discs. A music store has compact discs on sale for either $10$ or $$ 15 .$ A customer wants to spend at least $30$ but no more than $60$ on CDs at the store. Use the illustration to graph a system of inequalities that will show the possible combinations of the number of $10$ CDs $(x)$ and the number of $\$ 15 \mathrm{CDs}(y)$ that the customer can buy. Give two possible solutions. (GRAPH CANNOT COPY)

Compact Discs. A music store has compact discs on sale for either $10$ or $$ 15 .$ A
customer wants to spend at least $30$ but no more than $60$ on CDs at the store. Use the illustration to graph a system of inequalities that will show the possible combinations of the number of $10$ CDs $(x)$ and the number of $\$ 15 \mathrm{CDs}(y)$ that the customer can buy. Give two possible solutions.
(GRAPH CANNOT COPY)

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Key Concepts

Translation of Real-World Situations into Mathematical Models

This key concept focuses on the ability to interpret a practical problem and convert it into an algebraic form. It requires identifying the variables involved, establishing the relationships and constraints between them, and formulating a system of equations or inequalities that accurately represents the scenario.

System of Linear Inequalities

This concept involves setting up and solving multiple inequality expressions that must be satisfied at the same time. In many word problems, various conditions are provided which can be modeled with inequalities, forming a system where each inequality represents a constraint stemming from the scenario.

Graphical Representation of Inequalities

Graphing inequalities involves drawing each inequality on a coordinate plane by first graphing the related equation and then shading the region that satisfies the inequality. The intersection of the shaded areas from each inequality determines the overall solution set.

Feasible Region

The feasible region is the area on the graph where all the constraints are met simultaneously. This is the set of all possible solutions that satisfy the system of inequalities and is crucial for understanding the potential combinations that can be drawn from the constraints.

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