Ben creates a pattern using the rule “add 5.” Laura creates a pattern using the rule “add 10.”
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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 = × 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