– ALGEBRA I – Unit 1 – Section 2 Consecutive 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

– ALGEBRA I – Unit 1 – Section 2 Integer 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

Consecutive Integer Problems Let’s go through some examples. – 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.

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.

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.

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. 20 21 22 +1 +2 +1 +2 N N + 1 N + 2 Note that we follow the same “addition” procedure.

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

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

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

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.

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.

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. 20 22 24 +2 +4 +2 +4 N N + 2 N + 4 Note that we follow the same “addition” procedure.

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

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

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

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.

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.

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. 21 23 25 +2 +4 +2 +4 N N + 2 N + 4 Note that we follow the same “addition” procedure.

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

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

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

Try This Problem… Use the procedures that we just went through to the solve the following problems. The sum of four consecutive even integers is 268. Find the numbers. (Possible solutions for the first number: 60, 64, or 70) 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.

ALGEBRA IS FUN AND EASY! **Answers: 1) 64, 66, 68, and 70 2) 11 and 13