Section P8 Modeling with Equations 1

Problem Solving with Equations Step 1: Read the problem carefully. Attempt to state the problem in your own words and state what the problem is looking for. Let any variable represent one of the quantities in the problem. Step2: If necessary, write expressions for any other unknown quantities in the problem in terms of x. Step 3: Write an equation in x that models the verbal conditions of the problem. Step 4: Solve the equation and answer the problem’s question. Step 5: Check the solution in the original wording of the problem, not in the equation obtained from the words. 2

Example Spice Drops candy calorie count exceeds Smarties candy calorie count by 70 calories per serving. If the sum of one serving of each candy equals 170 calories find the calorie count of each kind of candy. Step 1: Represent one of the quantities Step 2: Represent the other quantity. Step 3:Write an equation in x that models the conditions. Step 4: Solve the equation and answer the question. Step 5: check the proposed solution. 3

Example A local telephone company charges $11 for local phone service and an additional $ .10 for each long distance phone call. A second local telephone company charges $14 for local service and an additional $ .05 for each long distance phone call. For how many minutes of long-distance calls will the costs for the two companies be the same? 4

Example In 2002, the median annual income for people with an advanced college degree was $73,000. This is a 170% increase over the median income in 1982 of people with an advanced degree. What were people with an advanced college degree making in 1982? 5

Example 30 feet 50 feet 6

Example 42 inches 25 inches 7

Example 25 feet 12 feet 8

P. 106 #7 – 47 e.o.o.