– algebra i – unit 1 – section 2 consecutive integer problems in order to work with a...
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![Page 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](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/1.jpg)
– 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 Consecutive means: “In a row” or “In order.”
![Page 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](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/2.jpg)
– 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:
Integer An integer is: a nice, round, positive/negative
number.
![Page 3: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/3.jpg)
– 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.
Let’s go through
some examples.
![Page 4: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/4.jpg)
Example ProblemsConsecutive 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
Notice that to get from the first number in the list to the second, we need to add 1.
+1
![Page 5: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/5.jpg)
Example ProblemsConsecutive 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
To get from the first number in the list to the third, we need to add 2.
+1 +2
![Page 6: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/6.jpg)
Example ProblemsConsecutive Integer Problem
The sum of three consecutive integers is 51. Find the numbers
• Instead of using numbers, we need to switch to variables.
20 21 22+1 +2
N• Note that we follow the same “addition” procedure.
+1 +2
N + 1 N + 2
![Page 7: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/7.jpg)
Example ProblemsConsecutive 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• Since we are looking for the sum, the equation is:
N + 1 N + 2
N + N + 1 + N + 2 = 51
![Page 8: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/8.jpg)
Example ProblemsConsecutive 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
![Page 9: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/9.jpg)
Example ProblemsConsecutive 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
N + 1 = 16 + 1 = 17
N + 2 = 16 + 2 = 18
Notice that the 3 solutions are integers, add up to 51, and are consecutive.
![Page 10: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/10.jpg)
Example ProblemsConsecutive 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
Notice that to get from the first number in the list to the second, we need to add 2.
+2
![Page 11: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/11.jpg)
Example ProblemsConsecutive 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
To get from the first number in the list to the third, we need to add 4.
+2 +4
![Page 12: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/12.jpg)
Example ProblemsConsecutive 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.
20 22 24+2 +4
N• Note that we follow the same “addition” procedure.
+2 +4
N + 2 N + 4
![Page 13: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/13.jpg)
Example ProblemsConsecutive 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• Since we are looking for the sum, the equation is:
N + 2 N + 4
N + N + 2 + N + 4 = 84
![Page 14: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/14.jpg)
Example ProblemsConsecutive 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
![Page 15: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/15.jpg)
Example ProblemsConsecutive 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
N + 2 = 26 + 2 = 28
N + 4 = 26 + 4 = 30
Notice that the 3 solutions are integers, even, add up to 84, and are consecutive.
![Page 16: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/16.jpg)
Example ProblemsConsecutive 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
Notice that to get from the first number in the list to the second, we need to add 2.
+2
![Page 17: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/17.jpg)
Example ProblemsConsecutive 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
To get from the first number in the list to the third, we need to add 4.
+2 +4
![Page 18: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/18.jpg)
Example ProblemsConsecutive 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.
21 23 25+2 +4
N• Note that we follow the same “addition” procedure.
+2 +4
N + 2 N + 4
![Page 19: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/19.jpg)
Example ProblemsConsecutive 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• Since we are looking for the sum, the equation is:
N + 2 N + 4
N + N + 2 + N + 4 = 57
![Page 20: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/20.jpg)
Example ProblemsConsecutive 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
![Page 21: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/21.jpg)
Example ProblemsConsecutive 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
N + 2 = 17 + 2 = 19
N + 4 = 17 + 4 = 21
Notice that the 3 solutions are integers, odd, add up to 57, and are consecutive.
![Page 22: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/22.jpg)
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)
**The answers can be found at the end of the PowerPoint.
2. The product of two consecutive odd integers is 143. Find the numbers. (Possible solutions for the first number: 9, 11, or 13)
![Page 23: – ALGEBRA I – Unit 1 – Section 2 Consecutive Integer Problems In order to work with a “consecutive integer” problems, we need to start by understanding](https://reader036.vdocuments.mx/reader036/viewer/2022062423/56649db05503460f94a9d76e/html5/thumbnails/23.jpg)
ALGEBRA IS FUN
AND EASY!**Answers: 1) 64, 66, 68, and 70 2) 11 and 13