A certain brand and style of shoe was priced at 120 . The...

A certain brand and style of shoe was priced at $\$ 120 .$ The store owner was concerned that this shoe was not selling well enough, so she decided to mark the list price down by $15 \%$. Sales of the shoe only increased slightly, so the owner offered an additional $10 \%$ discount from the sale price at checkout. Sales tax of $8 \%$ is added to all purchases. What would a customer have to pay for the shoes with tax added?

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Key Concepts

Multiplicative Reasoning

This concept involves understanding that successive percentage changes are applied through multiplication rather than addition. Each step in calculating the final price (discounts and tax) requires multiplying the current subtotal by a specific factor that represents either the remaining percentage or the additional percentage.

Sales Tax

Sales tax is an additional charge applied to the price of an item, calculated as a percentage of the sale price. After all discounts have been applied, the tax percentage is multiplied by the resulting amount, and then this tax is added to the price to obtain the final amount due.

Sequential Discounts

When multiple discounts are applied one after the other, each discount is calculated on the price obtained after the previous discount. This sequential application means that the overall discount is not simply the sum of the individual percentages, but rather reflects a multiplicative process.

Percentage Discounts

This concept involves reducing a price by a certain percentage. The discount is calculated by multiplying the original amount by the percentage (in decimal form), then subtracting that discount from the original amount to obtain the new price.

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