A storage closet holds twelve boxes stacked upon each other, with each box being 10 inches high. How many feet are there between the top of the third box and the bottom of the tenth box?
The Correct Answer and Explanation is:
Correct Answer: 5 feet
Explanation
To find the distance in feet between the top of the third box and the bottom of the tenth box, we must first understand the stacking arrangement and how height accumulates with each box.
Each box is 10 inches high, and there are 12 boxes stacked vertically.
Let’s visualize:
- The top of the third box means: from the bottom of the stack, we go up 3 boxes. Each box is 10 inches, so: Top of third box=3×10=30 inches from the bottom\text{Top of third box} = 3 \times 10 = 30 \text{ inches from the bottom}
- The bottom of the tenth box means: from the bottom, we go up 9 boxes. This is because the bottom of the tenth box lies right after the top of the ninth box, i.e., Bottom of tenth box=9×10=90 inches from the bottom\text{Bottom of tenth box} = 9 \times 10 = 90 \text{ inches from the bottom}
Now we find the distance between these two heights: Distance=90−30=60 inches\text{Distance} = 90 – 30 = 60 \text{ inches}
Since the problem asks for the answer in feet, and we know that: 12 inches=1 foot12 \text{ inches} = 1 \text{ foot}
We convert inches to feet: 6012=5 feet\frac{60}{12} = 5 \text{ feet}
Summary
The boxes are stacked directly on top of each other. The top of the third box is 30 inches from the bottom, and the bottom of the tenth box is 90 inches from the bottom. The difference is 60 inches, which equals 5 feet.
Thus, the distance between the top of the third box and the bottom of the tenth box is 5 feet.
