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Instructor Overview

Students connect percent to proportional relationships in the context of sales tax.

Key Concepts

  • When there is a constant tax percent, the total cost for items purchase—including the price and the tax—is proportional to the price.
  • To find the cost, c , multiply the price of the item, p, by (1 + t), where t is the tax percent, written as a decimal: c = p(1 + t).
  • The constant of proportionality is (1 + t) because of the structure of the situation:
    c = p + tp = p(1 + t).
  • Because of the distributive property, multiplying the price by (1 + t) means multiplying the price by 1, then multiplying the price by t, and then taking the sum of these products.

Goals and Learning Objectives

  • Find the total cost in a sales tax situation.
  • Understand that a proportional relationship only exists between the price of an item and the total cost of the item if the sales tax is constant.
  • Find the constant of proportionality in a sales tax situation.
  • Make a graph of an equation showing the relationship between the price of an item and the total amount paid.