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. The inequality to find the three numbers would be:
n + (n + 2) + (n + 4) > 84 and n + (n + 2) + (n + 4) < 96
b. Solving the inequality:
2n + 6 > 84 and 2n + 6 < 96
Subtract 6 from both sides of both inequalities:
2n > 78 and 2n < 90
Divide both sides of both inequalities by 2:
n > 39 and n < 45
The smallest even number, n, must be greater than 39 and less than 45.
Therefore, the three consecutive even numbers are:
n = 40, n + 2 = 42, and n + 4 = 44.