3.6 Equations and Problem
Solving
Date: ______________
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
Examples
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
Let
w = width
w=l-3
P = 26
w=8-3
w = 5 in
Perimeter Formula:
P = 2w + 2l
26 = 2(l – 3) + 2l
26 = 2l – 6 + 2l
26 = 4l – 6
32 = 4l
8=l
Examples
The sum of three consecutive integers is
72. Find the integers
Consecutive – in a row, back to back
n + n + 1 + n + 2 = 72
Let n = 1st number
n + 1 = 2nd number
3n + 3 = 72
n + 2 = 3rd number
-3 -3
3n = 69
3
3
n = 23
23, 24, 25
Examples
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?
Jet
Rate
Time
Distance
Traveled
1st
180
t
180t
2nd
330
t – 1 330(t – 1)
Let t = time the 1st plane travels
t – 1 = time the 2nd jet travels
180t = 330(t – 1)
180t = 330t – 330
- 330t - 330t
-150t = -330
t = 2.2
Examples
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
Up
4
t
Down
6
Distance
4t
Let t = time you go up the hill
Let 3 – t = time you go down
the hill
3 – t 6(3 – t)
4t = 6(3 – t)
4t = 18 – 6t
+ 6t
+ 6t
10t = 18
10t = 18
10 10
t = 1.8 h