Name: ____________________________________
Date: __________________
Word Problems Involving Consecutive Integers
In this lesson, we will explore consecutive integers, consecutive even integers, consecutive odd
integers, and word problems that contain these types of numbers.
Exercise #1: Determine the next two consecutive integers in each case.
(a) 5,  4,  3, _____, _____
(b) 12,13,14, _____, _____
(c) x, _________, _________
(Assume x is an integer.)
Exercise #2: Determine the next three consecutive even integers in each case.
(a) 18,  16,  14, _____, _____
(b) 20, 22, _____, _____
(c) x, _________, _________
(Assume x is an
even integer.)
Exercise #3: Determine the next three consecutive odd integers in each case.
(a) 13,  11,  9, _____, _____
(b) 5,  3,  1, _____, _____
(c) x, _________, _________
(Assume x is an
odd integer.)
Part (c) of each exercise above illustrates how we should define our variables when we seek to find
consecutive integers that meet certain criteria. We will now apply this work to solve a variety of
consecutive integer problems algebraically.
Exercise #4: If x  3 represents an integer, then the next consecutive integer in terms of x is
(1) x
(2) x  2
(3) x  4
(4) x  5
Exercise #5: If x  4 represents an odd integer, then the next consecutive odd integer in terms of x is
(1) x  6
(2) x  4
(3) x  3
(4) x  2
Exercise #6: If x  2 represents an odd integer, then the next larger even integer in terms of x is
(1) x  4
(2) x  3
(3) x  1
(4) x
Exercise #7: Find two consecutive integers such that their sum is 89. Only an algebraic solution will
be accepted.
For exercises 8 – 11, solve each algebraically.
Exercise #8: Find two consecutive integers such that the larger is nine more than twice the smaller.
Exercise #9: Find three consecutive even integers such that the sum of twice the first and three times
the third is fourteen more than four times the second.
Exercise #10: Three sisters have ages that are consecutive odd integers. Find the ages if the sum of
the age of the youngest and three times the age of the oldest is five less than five times the middle
sister’s age.
Exercise #11: Find three consecutive odd integers such that eight more than the sum of the first two is
equal to eleven less than three times the third.
Name: ____________________________________
Date: __________________
Word Problems Involving Consecutive Integers
Homework
Skills
1. If x represents an integer, then the next consecutive integer in terms of x is
(1) x
(2) x  1
(3) x  2
(4) x  3
2. If x  8 represents an even integer, then the next consecutive even integer in terms of x is
(1) x 10
(2) x  9
(3) x  7
(4) x  6
3. If x  2 represents an odd integer, then the next consecutive odd integer in terms of x is
(1) x  1
(2) x  3
(3) x  4
(4) x  5
For #4-10, solve each algebraically.
4. Find two consecutive integers that have a sum of 67.
5. Find three consecutive even integers such that their sum is 42.
6. Find three consecutive odd integers that have an average of 13.
7. Find two consecutive even integers such that twice the smaller diminished by twenty is equal to the
larger.
8. Find three consecutive odd integers such that twice the sum of the first and third exceeds the second
by fifteen.
9. Find three consecutive integers such that the sum of twice the second and three times the third is
five less than six times the first.
10. Three brothers have ages that are consecutive odd integers. The difference between the age of the
oldest and twice the age of the youngest is twenty-four less than the middle brother’s age. Find
their ages.
Reasoning
11. Explain why x and x  1 cannot represent two consecutive odd integers.
12. Suppose that n and n  1 represent two consecutive integers.
(a) Represent their sum in terms of n in simplest form.
(b) Explain why this sum must always be odd.