1
ALGEBRA I Unit 1 Section 2
Consecutive Integer Problems
In order to work with a consecutive integer
problems, we need to start by understanding the
terminology
Consecutive means In a row or In order.
Consecutive
2
ALGEBRA I Unit 1 Section 2
Consecutive Integer Problems
In order to work with a consecutive integer
problems, we need to start by understanding the
terminology
An integer is a nice, round, positive/negative
number.
Integer
3
ALGEBRA I Unit 1 Section 2
Consecutive Integer Problems
The key thing to remember is that your answers
will be consecutive integers. In other words,
the numbers you get should be nice (a.k.a. no
fractions or decimals) and they should be in a
row.
Lets go through some examples.
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Example Problems
Consecutive Integer Problem
The sum of three consecutive integers is 51.
Find the numbers

• The first thing to note is that we are dealing
  with consecutive integers.

• An example (that is not necessarily the solution)
  of consecutive integers could be

20
21
22
1
Notice that to get from the first number in the
list to the second, we need to add 1.
5
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers is 51.
Find the numbers

• The first thing to note is that we are dealing
  with consecutive integers.

• An example (that is not necessarily the solution)
  of consecutive integers could be

20
21
22
1
2
To get from the first number in the list to the
third, we need to add 2.
6
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers is 51.
Find the numbers

• Instead of using numbers, we need to switch to
  variables.

1
2
N
N 1
N 2

• Note that we follow the same addition
  procedure.

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Example Problems
Consecutive Integer Problem
The sum of three consecutive integers is 51.
Find the numbers

• Now to start the problem, we begin by writing the
  expressions for the THREE integers

N
N 1
N 2

• Since we are looking for the sum, the equation
  is

N N 1 N 2 51
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Example Problems
Consecutive Integer Problem
The sum of three consecutive integers is 51.
Find the numbers

• Suppose that the possible solutions for the first
  number are 15, 16, or 17. Guess and test to
  solve

(15) (15) 1 (15) 2 15 16 17 48 ?
51
(16) (16) 1 (16) 2 16 17 18 51
51
(17) (17) 1 (17) 2 17 18 19 54 ?
51
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Example Problems
Consecutive Integer Problem
The sum of three consecutive integers is 51.
Find the numbers

• Since 16 is the solution for the FIRST number in
  the list, the complete solution is

N 16
Notice that the 3 solutions are integers, add up
to 51, and are consecutive.
N 1 16 1 17
N 2 16 2 18
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Example Problems
Consecutive EVEN Integer Problem
The sum of three consecutive EVEN integers is 84.
Find the numbers

• The first thing to note is that we are dealing
  with consecutive EVEN integers.

• An example (that is not necessarily the solution)
  of consecutive integers could be

20
22
24
2
Notice that to get from the first number in the
list to the second, we need to add 2.
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Example Problems
Consecutive EVEN Integer Problem
The sum of three consecutive EVEN integers is 84.
Find the numbers

• The first thing to note is that we are dealing
  with consecutive integers.

• An example (that is not necessarily the solution)
  of consecutive integers could be

20
22
24
2
4
To get from the first number in the list to the
third, we need to add 4.
12
Example Problems
Consecutive EVEN Integer Problem
The sum of three consecutive EVEN integers is 84.
Find the numbers

• Instead of using numbers, we need to switch to
  variables.

2
4
N
N 2
N 4

• Note that we follow the same addition
  procedure.

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Example Problems
Consecutive EVEN Integer Problem
The sum of three consecutive EVEN integers is 84.
Find the numbers

• Now to start the problem, we begin by writing the
  expressions for the THREE integers

N
N 2
N 4

• Since we are looking for the sum, the equation
  is

N N 2 N 4 84
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Example Problems
Consecutive EVEN Integer Problem
The sum of three consecutive EVEN integers is 84.
Find the numbers

• Suppose that the possible solutions for the first
  number are 22, 24, or 26. Guess and test to
  solve

(22) (22) 1 (22) 2 22 24 26 72 ?
84
(24) (24) 1 (24) 2 24 26 28 78 ?
84
(26) (26) 1 (26) 2 26 28 30 84
84
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Example Problems
Consecutive EVEN Integer Problem
The sum of three consecutive EVEN integers is 84.
Find the numbers

• Since 26 is the solution for the FIRST number in
  the list, the complete solution is

N 26
Notice that the 3 solutions are integers, even,
add up to 84, and are consecutive.
N 2 26 2 28
N 4 26 4 30
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Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD integers is 57.
Find the numbers

• The first thing to note is that we are dealing
  with consecutive ODD integers.

• An example (that is not necessarily the solution)
  of consecutive integers could be

21
23
25
2
Notice that to get from the first number in the
list to the second, we need to add 2.
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Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD integers is 57.
Find the numbers

• The first thing to note is that we are dealing
  with consecutive integers.

• An example (that is not necessarily the solution)
  of consecutive integers could be

21
23
25
2
4
To get from the first number in the list to the
third, we need to add 4.
18
Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD integers is 57.
Find the numbers

• Instead of using numbers, we need to switch to
  variables.

2
4
N
N 2
N 4

• Note that we follow the same addition
  procedure.

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Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD integers is 57.
Find the numbers

• Now to start the problem, we begin by writing the
  expressions for the THREE integers

N
N 2
N 4

• Since we are looking for the sum, the equation
  is

N N 2 N 4 57
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Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD integers is 57.
Find the numbers

• Suppose that the possible solutions for the first
  number are 17, 19, or 21. Guess and test to
  solve

(17) (17) 1 (17) 2 17 19 21 57
57
(19) (19) 1 (19) 2 19 21 23 63 ?
57
(21) (21) 1 (21) 2 21 23 25 69 ?
57
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Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD integers is 57.
Find the numbers

• Since 17 is the solution for the FIRST number in
  the list, the complete solution is

N 17
Notice that the 3 solutions are integers, odd,
add up to 57, and are consecutive.
N 2 17 2 19
N 4 17 4 21
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Try This Problem
Use the procedures that we just went through to
the solve the following problems.

1. The sum of four consecutive even integers is 268.
   Find the numbers. (Possible solutions for the
   first number 60, 64, or 70)

1. The product of two consecutive odd integers is
   143. Find the numbers. (Possible solutions for
   the first number 9, 11, or 13)

The answers can be found at the end of the
PowerPoint.
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ALGEBRA IS FUN AND EASY!
Answers 1) 64, 66, 68, and 70 2) 11 and 13