NAME ______________________________________
DATE
PERIOD
Enrich
Consecutive Integer Problems
Many types of problems and puzzles involve the idea of consecutive
integers. Knowing how to represent these integers algebraically can
help to solve the problem.
EXAMPLE Find four consecutive odd integers whose sum is –80.
An odd integer can be written as 2n + 1, where n is any integer.
If 2n + 1 is the first odd integer, then add 2 to get the next largest odd
integer, and so on.
Now write an equation to solve this problem.
(2n + 1) + (2n + 3) + (2n + 5) + (2n + 7) = –80
Exercises
Write an equation for each problem. Then solve.
1. Complete the solution to the problem in the example.
-23, -21, -19, -17
2. Find three consecutive even integers whose sum is 132.
2n + (2n + 2) + (2n + 4) = 132; n = 21;
42, 44, 46
3. Find two consecutive integers whose sum is 19.
n + (n + 1) = 19; 9, 10
4. Find two consecutive integers whose sum is 100.
n + (n + 1) = 100; no solution
5. The lesser of two consecutive even integers is 10 more than
one-half the greater. Find the integers.
2n = 10 + (2n + 2); 22 and 24
6. The greater of two consecutive even integers is 6 less than three
times the lesser. Find the integers.
2n + 2 = 3(2n) - 6; 4, 6
7. Find four consecutive integers such that twice the sum of the two
2[(n + 2) + (n + 3)] = 3n + 91; 81, 82,
greater integers exceeds three times the first by 91.
83, 84
8. Find a set of four consecutive positive integers such that the
greatest integer in the set is twice the least integer in the set.
Course 2 • Chapter 6 Equations and Inequalities
n + 3 = 2n; 3, 4, 5, 6
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