Connecting Percentage To Proportional RelationshipsStudent View (Opens in new window)
Students connect percent to proportional relationships in the context of sales tax.
- 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.