Question

The bottom of Ignacio's desktop is
\[74.5\,\text{cm}\] from the floor. Ignacio sits in his adjustable chair, and the tops of his legs are
\[49.3\,\text{cm}\] from the floor. Each clockwise rotation of the knob on the chair raises Ignacio's legs by
\[4.8\,\text{cm}\].
What is the solution set of the inequality?
\[r\]

Answer 1

Let r be the number of clockwise rotations. After r rotations the leg height is 49.3 + 4.8r cm. To keep the tops of his legs at or below the bottom of the desk (74.5 cm) we need
49.3 + 4.8r ≤ 74.5.
Subtract 49.3: 4.8r ≤ 25.2, so r ≤ 25.2/4.8 = 5.25.

Thus r ≤ 5.25. Since r is a (nonnegative) number of full rotations, the possible whole-rotation values are
r ∈ {0,1,2,3,4,5}.