The bottom of Ignacio's desktop is 74.5cm from the floor. Ignacio sits in his adjustable chair, and the tops of his legs are 49.3cm from the floor. Each clockwise rotation of the knob on the chair raises Ignacio's legs by 4.8cm. Write an inequality to determine the number of clockwise rotations, r, Ignacio could make with the knob without his legs touching the desk.

Question

The bottom of Ignacio's desktop is  74.5cm from the floor. Ignacio sits in his adjustable chair, and the tops of his legs are  49.3cm from the floor. Each clockwise rotation of the knob on the chair raises Ignacio's legs by  4.8cm. Write an inequality to determine the number of clockwise rotations,  r, Ignacio could make with the knob without his legs touching the desk.

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Identify Heights: Identify the initial height of Ignacio's legs and the height of the desk. Ignacio's legs are initially 49.3cm from the floor, and the desk is 74.5cm from the floor.Calculate Max Increase: Calculate the maximum height increase for Ignacio's legs to not touch the desk. The maximum height Ignacio's legs can be raised is the difference between the desk height and the initial leg height. Maximum height increase = Desk height - Initial leg height Maximum height increase = 74.5cm - 49.3cm Maximum height increase = 25.2cmDetermine Height Per Rotation: Determine the height increase per rotation of the knob. Each rotation raises Ignacio's legs by 4.8cm.Write Inequality: Write an inequality to find the maximum number of rotations, r, without exceeding the maximum height increase. Let r be the number of rotations. Each rotation raises the height by 4.8cm, so 4.8cm * r should not exceed the maximum height increase of 25.2cm. 4.8r ≤ 25.2Check Inequality: Check the inequality to ensure it represents the situation correctly. The inequality 4.8r ≤ 25.2 means that the total height increase from rotating the knob (4.8cm per rotation times the number of rotations) should be less than or equal to the maximum allowable height increase (25.2cm). This correctly represents the situation.

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