Formulas frequently appear in the business world. For...

Formulas frequently appear in the business world. For example, the cost, $C,$ of an item (the price paid by a retailer) plus the markup, $M,$ on that item (the retailer's profit) equals the selling price, $S,$ of the item. The formula is $$C+M=S$$ The selling price of a television is $\$ 650 .$ If the cost to the retailer for the television is $\$ 520,$ find the markup.

Formulas frequently appear in the business world. For example, the cost, $C,$ of an item (the price paid by a retailer) plus the markup, $M,$ on that item (the retailer's profit) equals the selling price, $S,$ of the item. The formula is
$$C+M=S$$
The selling price of a television is $\$ 650 .$ If the cost to the retailer for the television is $\$ 520,$ find the markup.

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Key Concepts

Linear Equations

Linear equations represent relationships where variables are related through addition, subtraction, multiplication, and division. In many practical contexts, including business, these equations allow one to solve for an unknown quantity when the relationships between the known quantities are linear. This concept is fundamental when working with equations that need simple algebraic manipulation to isolate a particular variable.

Substitution

Substitution is an algebraic technique where numerical values are inserted in place of their corresponding variables in an equation. This method allows one to turn a general formula into a specific numerical equation that can be solved to find the unknown quantity. It is a core technique in problem-solving across mathematics and applied fields.

Markup Pricing

Markup pricing is a business concept where the selling price of an item is determined by adding the cost to produce or purchase an item and the profit margin. This concept is evident when setting prices in a retail environment, ensuring that costs are covered and a profit is generated based on the formula: cost plus markup equals selling price.

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