1. 1.3 Modeling with Linear Equations
In other words…..
Word Problems

2. 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!!!

3. 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?

4. 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

5. 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?

6. 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)

7. 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?

8. 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)

9. 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)

10. 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

11. 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.

12. 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 =

13. 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.

14. 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

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