Question

Three consecutive even numbers have a sum between 84 and 96.

a. Write an inequality to find the three numbers. Let n represent the smallest even number.
b. Solve the inequality.


a. 84 ≤ n + (n + 2) + (n + 4) ≤ 96
b. 78 ≤ n ≤ 90


a. 84 < n + (n + 2) + (n + 4) < 96
b. 26 < n < 30


a. 84 < n + (n + 1) + (n + 2) < 96
b. 27 < n < 31


a. n + (n + 2) + (n + 4) < –84 or n + (n + 2) + (n + 4) > 96
b. n < –30 or n > 31

Answer 1

a. 84 < n + (n + 2) + (n + 4) < 96

b. 26 < n < 30

Explanation:

Using 'n' to represent the smallest even number, the next even number would be 'n + 2' and the next even number would be 'n + 4'. So, the expression to represent three consecutive even numbers is: n + (n + 2) + (n + 4).

Since the sum of the these numbers needs to be between 84 and 96, we can set up the following inequality:

84 < n + (n + 2) + (n + 4) < 96

In order to solve for 'n', we must first combine like terms:

84 < 3n + 6 < 96

Subtract 6 from all sides: 84 - 6 < 3n + 6 - 6 < 96 - 6 or 78 < 3n < 90

Divide 3 by all sides: 78/3 < 3n/3 < 90/3 or 26 < n < 30.