EQUATION

1

EQUATION WORD PROBLEMS

LESSON 4
2
Steps to Solving Word Problems

• Use a variable to represent the unknown quantity
• Express any other unknown quantities in terms of
  this variable, if possible.
• Write an equation, and solve it.
• State the answer to the problem.
• Check your answer by substituting in the problem.
• If Age question, use a chart to organize
  information.
• If a distance, time, speed question, use a chart
  to organize information.

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Example 1
The sum of two consecutive odd numbers is 32.
What are the numbers
Let x represent the one number. Let (x 2 )
represent the other number.

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
x (x 2) 32
x (x 2) 32 2x 2 32 2x 2 - 2 32 -
2 2x 30
2x 2
30 2
x 15 x 2 17

4

YOU TRY!!
The sum of two consecutive even numbers is 34.
What are the numbers

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
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SOLUTION
The sum of two consecutive even numbers is 34.
What are the numbers
Let x represent the one number. Let (x 2 )
represent the other number.

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
x (x 2) 34
x (x 2) 34 2x 2 34 2x 2 - 2 34 -
2 2x 32
2x 2
32 2
x 16 x 2 18

6

Example 2
You have 3 less nickels than dimes. If you have
1.05, how many dimes do you have?
(Money Question)
Let x represent the number of dimes. Let (x - 3)
represent the number of nickels.

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
0.1x 0.05(x - 3) 1.05
0.1x 0.05x - 0.15 1.05 0.15x - 0.15
1.05 0.15x - 0.15 0.15 1.05 0.15 0.15x
1.20
0.15x 0.15
1.20 0.15
x 8

7

YOU TRY!!
You have 6 less nickels than quarters. If you
have 2.40, how many quarters do you have?
(Money Question)

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
8

Solution
You have 6 less nickels than quarters. If you
have 2.40, how many quarters do you have?
(Money Question)
Let x represent the number of quarters. Let (x -
6) represent the number of nickels.

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
0.25x 0.05(x - 6) 2.40
0.25x 0.05x - 0.3 2.40 0.3x - 0.3 2.40 0.3x
- 0.3 0.3 2.40 0.3 0.3x 2.70
0.3x 0.3
2.70 0.3
x 9

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Example 3
Jim ran 1.3 times faster than Bill during the 100
m dash. The difference in their speed was 18 m /
h. Find the speed of each racer.
(Distance, speed, NO TIME)
Let x represent the speed of Bill. Let 1.3x
represent the speed of Jim.

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
1.3x - x 18
1.3x - x 18 0.3x 18
0.3x 0.3
18 0.3

x 60 m / h 1.3x 78 m / h
10

YOU TRY!!
Jill biked 2.1 times faster than Amy during a
race. The difference in their speed was 22 km /
h. Find the speed of each racer.
(Distance, speed, NO TIME)

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
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Solution
Jill biked 2.1 times faster than Amy during a
race. The difference in their speed was 22 km /
h. Find the speed of each racer.
(Distance, speed, NO TIME)
Let x represent the speed of Amy. Let 2.1x
represent the speed of Jill.

Things to Remember Use a variable to represent
the unknown quantity Express any other unknown
quantities in terms of this variable, if
possible. Write an equation, and solve
it. State the answer to the problem. Check your
answer by substituting in the problem.
Equation
2.1x - x 22
2.1x - x 22 1.1x 22
1.1x 1.1
22 1.1

x 20 km / h 2.1x 42 km/ h
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Class Work

• Pass in Lesson 3(3) - Equation Word Problem
  Assignment.
• Copy down examples
• Complete Lesson 4 (Page 169 - 13-17)