Students create equations, tables, and graphs to show the proportional relationships in sales tax situations.
- The quantities—price, tax, and total cost—can each be known or unknown in a given situation, but if you know two quantities, you can figure out the missing quantity using the structure of the relationship among them.
- If either the price or the total cost are unknown, you can write an equation of the form y = kx, with k as the known value (1 + tax), and solve for x or y.
- If the tax is the unknown value, you can write an equation of the form y = kx and solve for k, and then subtract 1 from this value to find the tax (as a decimal value).
Building a general model for the relationship among all three quantities helps you sort out what you know and what you need to find out.
Goals and Learning Objectives
- Make a table to organize known and unknown quantities in a sales tax problem.
- Write and solve an equation to find an unknown quantity in a sales tax problem.
- Make a graph to represent a table of values.
- Determine the unknown amount—either the price of an item, the amount of the sales tax, or the total cost—in a sales tax situation when given the other two amounts.