Working With Percentages

Focus Question:

How can we use proportions and the constant of proportionality to solve problems involving percentages?

Part 1:  What is a Percentage?

So...remember that a percentage is just another type of special ratio.  The key characteristics of a percentage are:

• It is a part to whole ratio.
• The "whole" is always equal to 100.

Part 2: How to Solve Percentage Problems?

There are a couple of different ways to solve problems involving percentages.  We can set-up a pair of part to whole ratios, we can use a table to organize our thinking or we can construct equations in the form y=kx where "k" represents the percentage written in the form of a decimal.

For the problem below, try to set-up a table to organize your thinking.  Be really thoughtful about how each value is connected to the other values. (This is where the percentage work comes in).  In case you are not familiar with the language, here are some definitions to help you out:

• Purchase Price - the amount that Carla paid to get the car.
• Markup - the amount that Carla has increased the price of the car by in order to make a profit.  In this case, the markup is equal to 10% of the purchase price.
• Selling Price - the amount that Carla is going to sell the car for.  This is usually equal to the purchase price + markup.

Now, try to write an equation for each of the following relationships.  Remember that "k" is the percentage as a decimal.

• The markup based on the purchase price.
• The selling price based on the purchase price.
• The selling price based on the markup.

What you MUST do before next class:

• Finish TOFU for your Mid-Unit Assessment
• ACE (1-6) (11 OR 12) p. 71