1.3 Modeling with Linear Equations In other words….. Word Problems

Solving Real Life Problems! Step 1: Write a Verbal Model Ex. Distance = Rate x Time Step 2: Create Labels Ex. Distance = 20 miles Rate = r Time = .2 hours Step 3: Write and Solve Algebraic Model Ex. 20 = .2r Step 4: ANSWER THE QUESTION!!!

Example 1 You have accepted a job for which your annual salary will be $32,300. This salary includes year end bonus of $500. You will be paid twice in one month. What will your gross pay (pay before taxes) be for each paycheck?

Example 1 Continued Verbal Model Income for year = 24 Paychecks + Bonus Labels Income for year = $32,300 Amount of each paycheck = x Bonus = $500 Algebraic Model 32,300 = 24x + 500

Example 2 You have accepted a job that pays $8 an hour. You are told that after a two month probationary period, your hourly will be increased to $9 an hour. What percent raise will you receive after the two month period?

Example 2 Continued Verbal Model Raise = Percent x Old wage Labels New wage = $9 Raise = $9 - $8 = $1 Percent = x Algebraic Model 1 = x(8)

Example 3 Your family has an annual income of $57,000 and the following monthly expenses: mortgage ($1100), car payment ($375), food ($295), utilities ($240) and credit cards ($220). The total value of the monthly expenses represent what percent of your family’s annual income?

Example 3 Continued Verbal Model Monthly Expenses = Percent x Income For One Year Labels Income = 57,000 Monthly Expenses = 26,760 Percent = x Algebraic Model 26,760 = x(57,000)

Example 4 A rectangular kitchen is twice as long as it is wide, and its perimeter is 84 feet. Find the dimensions of the kitchen. (Find the length and the width)

Example 4 Continued Verbal Model 2(Length) + 2(Width) = Perimeter Labels Perimeter = 84 feet Width = w Length = 2w Algebraic Model 2(2w) + 2(w) = 84

Example 5 A plane is flying nonstop from Atlanta to Portland, a distance of about 2700 miles. After 1.5 hours in the air, the plane flies over Kansas City (a distance of 820 miles from Atlanta). Estimate the time it will take the plane to fly from Atlanta to Portland.

Example 5 Verbal Model Distance = Rate x Time Labels Distance = 2700 Time = t Rate = distance to Kansas City = time to Kansas City Algebraic Model 2700 =

Example 6 To determine the height of the Aon Center Building in Chicago, you measure the shadow cast by the building and find it to be 142 feet long. Then you measure the shadow cast by a four foot post and find it to be 6 inches long. Estimate the buildings height.

Example 6 Continued Verbal Model Height of building = Height of Post Length of Building’s Length of Post’s Shadow Shadow Labels Height of building = x Buildings shadow = 142 feet Height of post = 4 feet = 48 inches Post’s Shadow = 6 inches Algebraic Model

Homework Pg 107 #47-49,51-54, 57,62,63