1. Section 2.4 Formulas

2. Objectives Use formulas from business Use formulas from science Use formulas from geometry Solve for a specified variable

3. Objective 1: Use Formulas from Business A formula for retail price: To make a profit, a merchant must sell an item for more than he or she paid for it.  The price at which the merchant sells the product, called the retail price, is the sum of what the item cost the merchant plus the markup. Using r to represent the retail price, c the cost, and m the markup, we can write this formula as

4. Objective 1: Use Formulas from Business A formula for profit: The profit a business makes is the difference between the revenue (the money it takes in) and the cost. Using p to represent the profit, r the revenue, and c the cost, we can write this formula as

5. EXAMPLE 1 Estimates are that Warner Brothers made a $219 million profit on the film Harry Potter and the Half-Blood Prince. If the studio received $469 million in worldwide box office revenue, find the cost to make and distribute the film. (Source: www.the-numbers.com, June 2010) Films

6. Objective 2: Use Formulas from Science A formula for distance traveled: If we know the average rate (of speed) at which we will be traveling and the time we will be traveling at that rate, we can find the distance traveled. Using d to represent the distance, r the average rate, and t the time, we can write this formula as

7. EXAMPLE 3 As they migrate from the Bering Sea to Baja California, gray whales swim for about 20 hours each day, covering a distance of approximately 70 miles. Estimate their average swimming rate in miles per hour. (Source: marinebio.net) Whales

8. Objective 3: Use Formulas from Geometry To find the perimeter of a plane (two-dimensional, flat) geometric figure, such as a rectangle or triangle, we find the distance around the figure by computing the sum of the lengths of its sides.  Perimeter is measured in American units, such as inches, feet, yards, and in metric units such as millimeters, meters, and kilometers.

9. EXAMPLE 5 The largest flag ever flown was an American flag that had a perimeter of 1,520 feet and a length of 505 feet. It was hoisted on cables across Hoover Dam to celebrate the 1996 Olympic Torch Relay. Find the width of the flag. Flags

10. Objective 4: Solve for a Specified Variable Suppose a shopper wishes to calculate the markup m on several items, knowing their retail price r and their cost c to the merchant.  Given the formula r = c + m, a good way is to solve the formula for m first, substitute values for r and c, and then compute m directly. To solve a formula for a specified variable means to isolate that variable on one side of the equation, with all other variables and constants on the opposite side.

11. EXAMPLE 8 Solve the retail-price formula r = c + m for m.