A computer store budgets 12,000 to buy computers and laser...

A computer store budgets $\$ 12,000$ to buy computers and laser printers. Each computer costs $\$ 650$ and each printer costs $\$ 200$. (a) Let $C$ represent the number of computers and $P$ represent the number of printers. Write an equation that reflects the given situation. (b) Sketch the graph of this relationship. Be sure to label the coordinate axes clearly. (c) If the shipment contains 16 computers, use the equation you obtained in part (a) to find the number of printers.

A computer store budgets $\$ 12,000$ to buy computers and laser printers. Each computer costs $\$ 650$ and each printer costs $\$ 200$.
(a) Let $C$ represent the number of computers and $P$ represent the number of printers. Write an equation that reflects the given situation.
(b) Sketch the graph of this relationship. Be sure to label the coordinate axes clearly.
(c) If the shipment contains 16 computers, use the equation you obtained in part
(a) to find the number of printers.

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Key Concepts

Graphing Linear Equations

Graphing linear equations involves plotting the relationship between the two variables on a coordinate plane, usually by identifying key points such as intercepts. This visual representation aids in understanding the range of possible solutions and the constraints imposed by the equation.

Substitution Method

The substitution method is a technique used to solve equations by replacing one variable with a known value. This approach simplifies the process of finding the value of the other variable and is particularly useful in applied problems where one of the quantities is specified.

Budget Constraints

A budget constraint represents a limit on spending given available resources and is typically modeled by an equation that sums the costs of items to equal a total budget. This concept is crucial for understanding how to allocate resources within given limits and is commonly represented as a linear equation.

Linear Equations

A linear equation is a mathematical expression that shows a straight-line relationship between two variables. It is characterized by variables raised only to the first power and constant coefficients, making it ideal for modeling real-world problems such as the allocation of costs in budgeting scenarios.

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