1. 3.6 Equations and Problem Solving
Date: ______________

2. Steps to Solve Word Problems
Identify the unknowns
Use variables
Draw a diagram that will help you understand the problem
Determine the formulas, equations that the problem is dealing with
Might be more than one
Read a sentence at a time and make an equation

3. Examples Perimeter Formula: P = 2w + 2l w = l - 3 26 = 2l – 6 + 2l
The width of a rectangle is 3 in. less than its length. The perimeter of the rectangle is 26 in. What is the width of the rectangle.
Let l = length
Perimeter Formula:
P = 2w + 2l
Let
w = width
26 = 2(l – 3) + 2l
w = l - 3
26 = 2l – 6 + 2l
P = 26
26 = 4l – 6
w = 8 - 3
32 = 4l
w = 5 in
8 = l

4. Examples
The sum of three consecutive integers is 72. Find the integers
Consecutive – in a row, back to back
Let n = 1st number
n + n n + 2 = 72
n + 1 = 2nd number
3n + 3 = 72
n + 2 = 3rd number
3n = 69
n = 23
23, 24, 25

5. Examples 180t = 330(t – 1) 180t = 330t – 330 - 330t - 330t
An airplane left an airport flying at 180 mi/h. A jet that flies at 330 mi/h left 1 hour later. The jet follows the same route as the airplane at a different altitude. How many hours will it take the jet to catch up with the airplane?
Let t = time the 1st plane travels
Jet
Rate
Time
Distance Traveled
1st
2nd
t – 1 = time the 2nd jet travels
180 t
180t
180t = 330(t – 1)
330
t – 1
330(t – 1)
180t = 330t – 330
- 330t t
-150t = -330
t = 2.2

6. Examples 4t = 6(3 – t) 10t = 18 4t = 18 – 6t 10 10 + 6t + 6t t = 1.8 h
Suppose you hike up a hill at 4 km/h. You hike back down at 6 km/h. Your hiking trip took 3 hours. How much time did it take you to hike up the hill?
Hill
Rate
Time
Distance Up
Down
Let t = time you go up the hill
Let 3 – t = time you go down the hill 4 t 4t 6
3 – t
6(3 – t)
4t = 6(3 – t)
10t = 18
4t = 18 – 6t
+ 6t t
t = 1.8 h
10t = 18