Basic Algebra Series

Basic Algebra Word Problems Creating algebraic formulas from word problems involving consecutive integers

Read and Understand

• Read the problem carefully and create variables for each term described

• When the problem states that the integers are consecutive (one directly after the other), you would use a routine such as: x, x+1, x+2, x+3, etc. These are consecutive.

• If a problem states only odd or only even, these numbers always have a “skipped” number between; therefore, use: x, x+2, x+4, x+6, etc.

Two consecutive integers have a sum of 91. What are the two integers?

• How many integers and how are they spaced?

• 2 consecutive

• What will we do with the two terms?

• Sum them….add them together

• What will they equal?

• 91

• Create the variables using algebraic terms

• (x) and (x+1)

• Substitute them into the statement

• (x) + (x+1) = 91

Do the math (x) + (x+1) = 91

• Remove the parenthesis, they are not needed in simple addition

• x + x + 1 = 91

• How many x’s?

• 2x +1 = 91

• If we do the same thing to both sides of an equation, the equation remains equal!!!!!

• 2x + 1 – 1 = 91 – 1

• 2x = 90

• 2x/2 = 90/2

• x = 45

Substitute the value of x into the formula

• 45 + (45+1) = 91

• 45 + 46 = 91

• Yes they do!!!

• The answer is 45 and 46, those two numbers are consecutive and equal 91 when added together.

• The formula will always remain the same for a same scenario problem.

• Let’s try a few more!

The sum of two consecutive integers is 27, what are the two integers?

• (x)+(x+1)=27

• 2x +1 = 27

• 2x +1 -1 = 27 -1

• 2x = 26

• 2x/2 = 26/2

• x= 13

• x=13, x+1 = 14, ans: 13 & 14

• 13 + 14 = 27, tests true

The sum of two consecutive integers is 9. What are the two integers?

• 2x+1 = 9

• 2x = 8

• x = 4

• x+1 = 5

• 4 + 5 = 9, true

• What if both numbers need to be even?

• Even or odd means every other number

• x, x+2, x+4, etc.

• Let’s try a few!

Two consecutive even integers have a sum of 26. What are the two integers?

• (x) + (x+2) = 26

• x + x + 2 = 26

• 2x + 2 = 26

• 2x + 2 – 2 = 26 – 2

• 2x = 24

• 2x/2 = 24/2

• x = 12

• Replace value of x into formula

• (12)+ (12 + 2) = 26

• 12 + 14 = 26…true!

• Ans: 12 and 14

What two consecutive even numbers have a sum of 90?

• x + x + 2 = 90

• 2x + 2 = 90

• 2x = 88

• x = 44, x+2 = 46….ans: 44, 46

• 44 + 46 = 90 and they are both even.

• What if the integers need to be odd?

• The formula is the same.

• Let’s try a few examples

Two consecutive odd integers have a sum of 48. What are the two odd integers?

• (x) + (x+2) = 48

• 2x + 2 = 48

• 2x = 46

• x = 23, x + 2 = 25

• 23 + 25 = 48

• Ans: 23, 25

• They are both odd and they equal 48.

What two consecutive odd integers have a sum of 88?

• x + x + 2 = 88

• 2x + 2 = 88

• 2x = 86

• x = 43, x + 2 = 45

• 43 + 45 = 88

• Ans: 43, 45

• They equal 88 and are both odd.

• What about 3 or more consecutive numbers?

What three consecutive integers have a sum of 21?

• (x) + (x+1) + (x+2) = 21

• x + x +1 + x + 2 = 21

• Add up the x’s and the numbers

• 3x + 3 = 21

• 3x +3 – 3 = 21 – 3

• 3x = 18

• 3x/3 = 18/3

• x = 6, 6+1 = 7, 6+2= 8

• 6 + 7 + 8 = 21

• Ans: 6, 7, 8

• Let’s try one more of those.

What three consecutive integers have a sum of 33?

• x + x+1 + x+2 = 33

• 3x + 3 = 33

• 3x = 30

• x = 10

• Ans: 10, 11, 12

• 10 + 11 + 12 = 33

Consecutive negative integers

• The first term is always x regardless of negative or positive term.

• To increase the negativity of a number, you subtract.

• What is more negative than -5? Ans: -6

• What is more negative than x? Ans: x – 1

• How to count from -5 to 5

• -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5

• Notice that zero is neither negative or positive

• Let’s try a few of these!

Two negative consecutive integers have a sum of -21. What are the integers?

• (x) + (x-1) = -21

• x + x - 1 = -21

• 2x – 1 = -21

• 2x = -20

• 2x/2 = -20/2

• x = -10

• -10 -1 = -11

• (-10) + (-11) = -21

• -10 – 11 = -21

• The statement is true and both numbers are negative.

What two consecutive negative integers have a sum of -47?

• x + (x-1) = -47

• 2x – 1 = -47

• 2x = -46

• X = -23

• x-1 = -24

• Ans: -23, -24

• (-23) + (-24) = -47

Let’s do 3 consecutive even and 3 consecutive odd

What 3 consecutive even integers have a sum of 36? • (x) + (x+2) + (x+4) = 36

• 3x + 6 = 36

• 3x = 30

• x = 10

• (x+2) = 12, (x+4) = 14

• 10 + 12 + 14 = 36

• Ans: 10, 12, 14

What three consecutive odd integers have a sum of 57? • (x) + (x+2) + (x+4) = 57

• 3x + 6 = 57

• 3x = 51

• x/3 = 51/3

• x = 17

• (x +2 )= 19, (x + 4)= 21

• 17 + 19 + 21 = 57

• Ans: 17, 19, 21

• How about 3 consecutive negative numbers?

What 3 consecutive negative integers have a sum of -36?

• (x) + (x-1) + (x-2) = -36

• 3x - 3 = -36

• 3x - 3 + 3 = -36 + 3

• 3x = -33

• x = -11

• (x-1)= -12, (x-2) = -13

• (-11) + (-12) + (-13) = -36

• Ans: -11, -12, -13

• One more before we quit. Think about this one!

What 3 consecutive even integers have a sum of -36?

• (x) + (x-2) + (x-4) = -36

• 3x - 6 = -36

• 3x - 6 + 6 = -36 + 6

• 3x = -30

• x = -10

• (x-2) = -12, (x-4) = -14

• (-10) + (-12) + (-14) = -36

• Ans: -10, -12, -14

I hope you enjoyed this exercise of summing consecutive numbers. Algebra is a math that can be used in everyday life. The more you use it, the easier it gets.