Question

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

Answer 1

Answer:

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

b. 26 < n < 30

Step-by-step 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.