Section 2.4Formulas

Objectives

Use formulas from business Use formulas from science Use formulas from geometry Solve for a specified variable

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

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

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

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

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

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.

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

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.

EXAMPLE 8

Solve the retail-price formular = c + m for m.