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) 96

b. n 31

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

b. 26 < n < 30

Step-by-step explanation:

Let n = 1st number

n+2 2nd even number

n+4 = 3rd even number

The sum of these 3 numbers is

n+n+2+n+4

It must be between 84 and 96 (it does not include this 84 and 96)

84< n+n+2+n+4 < 96

Now we need to solve this

Combine like terms

84 < 3n + 6< 96

Subtract 6 from all sides

84 - 6 < 3n+6-6 < 96 - 6

78 < 3n < 90

Divide all sides by 3

78/3 < 3n/3 < 90/3

26 < n< 30