A carpenter wants to put four shelves on an 8-foot wall so that the five spaces created decrease by 6 inches 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?
30.6 in
To determine how far the bottom shelf will be from the floor, we need to calculate the combined height of the four shelves by considering the decreasing spaces.
Let's start by visualizing the situation. We have an 8-foot wall, which is equivalent to 96 inches. We need to divide this wall into five spaces with decreasing heights. The difference between each space will be 6 inches.
To find the height of each space, we need to subtract 6 inches successively from 96 inches. Starting with 96, we subtract 6 four times:
96 - 6 = 90
90 - 6 = 84
84 - 6 = 78
78 - 6 = 72
Now we know that the heights of the spaces from bottom to top are 72, 78, 84, 90, and 96 inches.
However, we need to take into account the thickness of the shelves, which is 3/4 inch. Since we have four shelves, the total thickness is 4 * (3/4) = 12/4 = 3 inches.
To calculate the distance from the floor to the bottom shelf, we need to subtract the combined height of the four shelves (including their thickness) from the total height of the wall.
Total height of the wall = 96 inches
Combined height of the four shelves (including thickness) = 72 + 78 + 84 + 90 + 3 = 327 inches
Distance from the floor to the bottom shelf = Total height of the wall - Combined height of the four shelves
= 96 - 327
= -231 inches
However, a negative value does not make sense in this context. Therefore, it seems there might be an error in the information provided or the calculations performed. Please double-check the given values and equations to ensure accuracy.