Question

A carpenter wants to put four shelves on a 8-foot wall(=b) so that the five spaces created decrease by 7 inches(=a) as we move up the wall. If the thickness of each shelf is
3/4 inch, how far will the bottom shelf be from the floor?

Answer 1

Height of wall = 8 feet

1 feet = 12 inches

⇒ Height of wall = 8 × 12 inches

⇒ Height of wall = 96 inches

We know that the 4 shelves are to be placed such that that the 5 spaces created decrease by 7 inches as we move up the wall

Let height of 1st space = h inches

⇒ Height of 2nd space = h - 7 inches

⇒ Height of 3rd space = h - 14 inches

⇒ Height of 4th space = h - 21 inches

⇒ Height of 5th space = h - 28 inches

Thickness of each shelf = 3/4 inch

⇒ Thickness of 4 shelves = $\frac{3}{4}$ × 4 inches = 3 inches

So, Height of Wall = Height of 1st space + Height of 2nd space + Height of 3rd space + Height of 4th space + Height of 5th space + Thickness of 4 shelves

⇒ 96 = h + h - 7 + h - 14 + h -21 + h - 28 + 3

⇒ 95 = 5h - 70 + 3

⇒ 95 = 5h - 67

⇒ 5h = 162

⇒ h = 32.4 inches

So the first shelf is placed 32.4 inches from the floor