Retail prices in a department store are obtained by marking...

Retail prices in a department store are obtained by marking up the wholesale price by $40 \%$. That is, retail price is obtained by adding $40 \%$ of the wholesale price to the wholesale price. (A) What is the retail price of a suit if the wholesale price is $\$ 300 ?$ (B) What is the wholesale price of a pair of jeans if the retail price is $\$ 77 ?$

Retail prices in a department store are obtained by marking up the wholesale price by $40 \%$. That is, retail price is obtained by adding $40 \%$ of the wholesale price to the wholesale price.
(A) What is the retail price of a suit if the wholesale price is $\$ 300 ?$
(B) What is the wholesale price of a pair of jeans if the retail price is $\$ 77 ?$

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Key Concepts

Solving Linear Equations

Solving linear equations is a fundamental concept used for determining unknown variables in relationships involving percentages. In problems involving price markups, setting up a linear equation allows one to solve for either the original value or the marked-up value by isolating the unknown variable through inverse operations, such as division or subtraction. This approach is essential for a wide range of mathematical and real-world applications.

Multiplicative Factor

The concept of a multiplicative factor is used to simplify the calculation of a percentage increase. Instead of computing the percentage of the original value and then adding it, one can multiply the original value by a factor (which is 1 plus the markup rate expressed as a decimal). This factor directly converts the wholesale price to the retail price, streamlining calculations.

Percentage Markup

Percentage markup involves increasing an original value by a given percentage of that value. This is a common technique in pricing, where the marked-up price (such as the retail price) is calculated by adding a set percentage of the original cost (such as the wholesale price) to that cost. Understanding percentage markup is essential for grasping how price adjustments are made in various fields like retail and finance.

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