There are two boards, a and b. The total length of both is 28 feet. Board b is at least 5 feet longer than board a, but the difference is not more than 12 feet. What are the possible lengths of the two boards?

Step-by-step explanation:

Let a represent the length of board a.

Let y represent the length of board b.

The total length of both is 28 feet. This means that

a + b = 28

Board b is at least 5 feet longer than board a. This means that

b ≥ a + 5

The difference between both boards is not more than 12 feet. This means that

b - a < 12

Substituting a = 28 - b into b ≥ a + 5, it becomes.

b ≥ 28 - b + 5

b ≥ 28 - b + 5

2b ≥ 28

b ≥33/2

b ≥ 16.5

16.5 - a < 12

4.5 < a

a > 4.5

The possible lengths of board a is

8 to 11.5 feet

The possible lengths of board b is

16.5 to 20 feet