Unit 3 Target 2.2
Consecutive Integer Story Problems
In order to work with a “consecutive integer” problems, we
need to start by understanding the terminology:
Consecutive: ___________________________________
Integer: ______________________________________
What do Consecutive Equations look like?
The first thing to note is that we are dealing with
consecutive integers.
20
21
22
Notice that to get from the first number in the list to the
second, we need to add 1. But from the first to the second
we add 2.
Setting Up Consecutive Integer Problems
Consecutive Integer Problems follow a pattern.
51
52
53
N = Value of 1st Integer in Sequence
N + N + 1 + N + 2 = Given Total
Example 1: The sum of three consecutive integers is 51.
Find the three numbers.
Example 3: The sum of three consecutive EVEN integers
is 84. Find the three numbers.
Write an Equation
Write an Equation
Solve Your Equation
Solve Your Equation
Final Answer
Final Answer
Example 2: The sum of three consecutive integers is 915.
Find the three numbers.
Example 4: The sum of three consecutive ODD integers is
57. Find the three numbers.
Write an Equation
Write an Equation
Solve Your Equation
Solve Your Equation
Final Answer
Final Answer
Unit 3 Target 2.2
Consecutive Integer Story Problems
Example: Twice the larger of two consecutive integers is
equal to fifteen less than three times the smaller. What are
the two integers?
Let’s break it down…first we decide what we know and
choose a variable.
Let’s go solving for the larger number.
1. N = Larger of the Two Consecutive Numbers
2. Twice the larger of the two consecutive numbers = 2n
3. Fifteen less than three times the smaller = 3(n – 1) – 15
Why (N – 1)?...if N is the larger of the two numbers than
(N-1) is the smaller of the two numbers.
4. Let’s put both equations together… 2n = 3(n – 1) - 15
5. Solve for N and we should get N = 18
6. Final Answer = 17, 18
Example 1: Five times the larger of two consecutive odd
integers is equal to one more than eight times the smaller.
Define a Variable
Solve Your Equation
Write an Equation
Final Answer
Example 3: Four times the larger of two consecutive odd
integers is seven less than five times the smaller. What
are the integers?
Solve Your Equation
Final Answer
Define a Variable
Write an Equation
Example 2: Ten times the larger of two consecutive even
integers minus seven times the smaller equals two times
the sum of the two integers. Find the integers.
Define a Variable
Solve Your Equation
Write an Equation
Final Answer