AlgebraAlgebra

3.53.5Consecutive Integer ProblemsConsecutive Integer Problems

Consider integers on a number Consider integers on a number line……..line……..

-5 -4 -3 -2 -1 0 1 -5 -4 -3 -2 -1 0 1 2 3 4 52 3 4 5 6 7 6 7

nn + 1

n + 2n + 3

Wherever you start, Wherever you start, consecutive integersconsecutive integers go up go up

1 at a time……..1 at a time……..-5 -5 -4 -3 -2 -1-4 -3 -2 -1 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

nn + 1

n + 2n + 3 Etc.

consecutive even integersconsecutive even integers go up 2 at a time……..go up 2 at a time……..

-5 -5 -4-4 -3 -3 -2-2 -1 -1 00 1 1 22 3 4 5 6 7 3 4 5 6 7

n

n + 2

n + 4n + 6

Etc.

and and consecutive odd consecutive odd integersintegers go up 2 at a go up 2 at a

time……..time……..-5-5 -4 -4 -3-3 -2 -2 -1-1 0 0 11 2 3 4 5 6 7 2 3 4 5 6 7

n

n + 2

n + 4n + 6

Etc.

Let’s try this problemLet’s try this problemThe sum of three consecutive integers is 39. Find The sum of three consecutive integers is 39. Find the integers.the integers.

a + b + c = 39

n + n + 1 + n + 2 = 39

3n + 3 = 393n = 36 n = 12

So a = 12, b = 13 and c = 14. They add to 39.

These are easy!These are easy!The sum of three consecutive odd integers is 87. The sum of three consecutive odd integers is 87. Find the integers.Find the integers.

a + b + c = 87

n + n + 2 + n + 4 = 87

3n + 6 = 873n = 81n = 27

So a = 27, b = 29 and c = 31. They add to 87.

Still Easy!Still Easy!The sum of four consecutive even integers is -4. The sum of four consecutive even integers is -4. Find the integers.Find the integers.

a + b + c + d = -4

n + n + 2 + n + 4 + n + 6 = -4

4n + 12 = -44n = -16 n = -4So a = -4, b = -2, c = 0, and d = 2. They add to -4.

Piece of Cake!Piece of Cake!Find four consecutive integers such that three times the Find four consecutive integers such that three times the second integer when decreased by 10 is equal to the second integer when decreased by 10 is equal to the sum of the third and fourth integers.sum of the third and fourth integers.

Using a, b, c and d:Using a, b, c and d:

3b - 10 = c + d

3 ( n + 1 ) - 10 = n + 2 + n + 3

3n + 3 - 10 = 2n + 5 3n - 7 = 2n +5 n = 12So a = 12, b = 13, c = 14, and d = 15. 3(13) – 10 = 14 + 15

Try this one……..Try this one……..Find three consecutive odd integers such Find three consecutive odd integers such that when twice the second integer is that when twice the second integer is increased by 10 it is equal to 7 less than increased by 10 it is equal to 7 less than three times the third integer.three times the third integer.

Set-up:Set-up: 2b + 10 = 3c - 72b + 10 = 3c - 7Equation: 2 (n + 2) + 10 = 3 (n+ 4) – 7Equation: 2 (n + 2) + 10 = 3 (n+ 4) – 7Solution: The numbers are 9, 11 and 13.Solution: The numbers are 9, 11 and 13.

HomeworkHomework