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Algebra: Consecutive
Integer Problems
Consecutive integer problems are word problems
that involve
CONSECUTIVE INTEGERS.
EXPLANATION
Consecutive integers are integers that
follow in sequence, each number being 1
more than the previous number,
represented by n, n +1, n + 2, n + 3, ...,
where n is any integer.
For example: 23, 24, 25, …
EVEN CONSECUTIVE INTEGERS
If we start with an EVEN NUMBER and each
number in the sequence is 2 more than
the previous number then we will get
consecutive even integers.
For example: 16,18, 20, …
If we start with an ODD NUMBER and each
number in the sequence is 2 more than
the previous number then we will get
consecutive odd integers.
For example: 33, 35, 37, …
BELL RINGER
YOU REPRESENT CONSECUTIVE EVEN
INTEGERS AS
n, n + 2, n + 4, n + 6, etc.
How do you represent
CONSECUTIVE ODD INTEGERS????
NEVER FORGET THIS!!!!!!
EXACTLY THE SAME WAY!!
n, n+2, n + 4, n + 6, etc.
EACH NUMBER IS STILL TWO
AWAY FROM THE NEXT!!
DO YOU SEE???
EXAMPLE ONE:
The sum of the least and
greatest of 3 consecutive
integers is 60. What are
the values of the 3
integers?
Solution:
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Step 1: Assign variables :
Let x = least integer
x + 1 = middle integer
x + 2 = greatest integer
Translate sentence into an equation.
Sentence: The sum of the least and greatest is
60.
• Rewrite sentence:
• x + (x + 2) = 60
Step 2:
Solve the equation
COMBINE like terms
2x + 2 = 60
ISOLATE variable x
2x =58
Step 3:
Check your answer
29 + 29 + 2 = 60
The question wants all the 3 consecutive
numbers: 29, 30 and 31
Answer: The 3 consecutive numbers are 29,
30 and 31.
Example 2: Consecutive
Odd Integer
The lengths of the sides of a
triangle are consecutive odd
numbers. What is the length of the
longest side if the perimeter is 45?
Solution:
Step 1: Being consecutive odd
numbers we need to add 2 to the previous
number.
Assign variables :
Let x = length of shortest side
x + 2 = length of medium side
x + 4 = length of longest side
Sketch the figure
Step 2:
Write out the formula
for PERIMETER OF A
TRIANGLE
P = sum of the three
sides
Step 3:
Plug in the values from the
question and from the sketch.
45 = x + x + 2 + x + 4
COMBINE like terms
45 = 3x + 6
ISOLATE variable x
3x = 45 – 6
3x = 39
x =13
Step 4:
Check your answer
13 + 13 + 2 + 13 + 4 = 45
Be careful! The question
requires the length of the
longest side.
The length of longest = 13 + 4
=17
Answer: The length of longest
side is 17
PRACTICE
Example 3: Consecutive
Even Integer
John has a board that is 6
feet long. He plans to use it
to make 4 shelves whose
lengths are to be a series of
consecutive even numbers.
How long should each shelf
be in inches?
ANSWER
The lengths of the
shelves should be 6, 8,
10 and 12.
PRACTICE
1. Find three consecutive odd integers
whose sum is the square of 6.
2. The greater of two consecutive integers
is 10 less than twice the smaller.