A clothing store sells a shirt costing 20 for 33 and a...

A clothing store sells a shirt costing $\$ 20$ for $\$ 33$ and a jacket costing $\$ 60$ for $\$ 93$. (A) If the markup policy of the store is assumed to be linear, write an equation that expresses retail price $R$ in terms of $\operatorname{cost} C$ (wholesale price). (B) What does a store pay for a suit that retails for $\$ 240 ?$

A clothing store sells a shirt costing $\$ 20$ for $\$ 33$ and a jacket costing $\$ 60$ for $\$ 93$.
(A) If the markup policy of the store is assumed to be linear, write an equation that expresses retail price $R$ in terms of $\operatorname{cost} C$ (wholesale price).
(B) What does a store pay for a suit that retails for $\$ 240 ?$

Key Concepts

Markup

Markup in a business context refers to the addition of a fixed amount or percentage to the cost of a product in order to determine its selling price. A linear markup model implies that the retail price increases at a constant rate with respect to the cost. Understanding markup is critical for pricing strategies and helps in establishing a predictable profit margin.

Solving Linear Equations

Once a linear relationship has been established, solving linear equations allows for determining one variable given a value of the other. This process involves algebraic manipulation of the equation, such as isolating the variable of interest, to find its corresponding value. This skill is essential for making predictions and understanding the underlying dynamics of the model.

Linear Modeling

This concept involves using a linear function to represent the relationship between two quantities. In many real-world contexts, especially in economics and business, a linear model assumes that changes in one variable correspond to proportional changes in another. It simplifies the relationship into a formula of the form y = mx + b, where the constants m and b represent the rate of change and the baseline offset, respectively.

Slope-Intercept Form

The slope-intercept form of a linear equation, y = mx + b, is a fundamental representation in algebra. The 'm' represents the slope of the line, indicating how much the dependent variable changes for a unit change in the independent variable, while 'b' is the y-intercept, the point where the line crosses the y-axis. This form is particularly useful for quickly identifying the behavior of a linear relationship in various applications.

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