The Squeaky Clean Window Cleaning Company has several costs...

The Squeaky Clean Window Cleaning Company has several costs included in cleaning windows for a business. The materials and cleaning solutions cost about $\$ 1.50$ per window. Insurance and salaries for the day will cost about $\$ 530 .$ a. Write an equation for the total cost to clean windows for a day depending on the number of windows cleaned. b. How much will it cost if the company cleans 60 windows? c. How many windows can the company clean if the total cost cannot exceed a budget of $\$ 800 ?$

The Squeaky Clean Window Cleaning Company has several costs included in cleaning windows for a business. The materials and cleaning solutions cost about $\$ 1.50$ per window. Insurance and salaries for the day will cost about $\$ 530 .$
a. Write an equation for the total cost to clean windows for a day depending on the number of windows cleaned.
b. How much will it cost if the company cleans 60 windows?
c. How many windows can the company clean if the total cost cannot exceed a budget of $\$ 800 ?$

Key Concepts

Substitution in Equations

Substitution is a method used to evaluate an equation by replacing the variable with a specific value. In the context of cost functions, substitution is used to compute the total cost for a given number of units by plugging the quantity into the linear cost function.

Function Modeling in Word Problems

This concept involves translating a real-world scenario into a mathematical expression. It requires identifying the fixed and variable components of the situation and combining them into an equation that represents the total cost based on the quantity involved.

Solving Linear Equations and Inequalities

This concept encompasses finding the value of the variable that satisfies an equation or inequality. For cost constraints, solving a linear inequality determines the maximum or minimum number of units that can be produced or processed without exceeding a budget.

Linear Equations

Linear equations model the relationship between two quantities where one quantity is directly proportional to the other. In cost problems, this often appears as a fixed cost plus a variable cost multiplied by the number of items or operations, resulting in an equation of the form y = mx + b.

Fixed and Variable Costs

Fixed costs are expenses that do not change with the level of production or service, such as salaries or insurance in this scenario. Variable costs change in direct proportion to the number of units produced or services rendered, like the per-window cleaning material costs in the problem.

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