Math Problem Statement
In an art museum, there is a wall that is 18 m 40 cm
wide. Eleven frames, each 80 cm wide, are hung on the
wall. How long is the interval between each frame
needed to make the distance between the left and right
ends of the wall and the frames the same?
Solution
We are given a wall that is 18 meters 40 centimeters (or 18.4 meters) wide. There are 11 frames, each 80 cm wide, which is equivalent to 0.8 meters per frame. We need to calculate the equal interval between each frame so that the distance from the left and right ends of the wall to the frames is the same.
Step 1: Total width of the frames
The total width of the 11 frames is:
Step 2: Remaining space on the wall
The total width of the wall is 18.4 meters, so the remaining space that is not occupied by the frames is:
Step 3: Number of gaps
There are 12 gaps in total (one between each pair of frames, and one on each end of the row).
Step 4: Width of each interval
To find the width of each interval between the frames, we divide the remaining space by the number of gaps:
Thus, the interval between each frame (and also between the ends of the wall and the nearest frame) should be 0.8 meters.
Do you need further details or have any questions?
Here are 5 related questions you could explore:
- How would the interval change if there were 10 frames instead of 11?
- What would be the interval if the wall was only 15 meters wide?
- If each frame was 90 cm wide, what would the new interval be?
- How much total space would be occupied by the frames if each one were 100 cm wide?
- If you wanted the interval to be exactly 1 meter, what would the new wall width need to be?
Tip: When calculating spacing for objects like frames, always ensure you account for the total number of gaps, which usually includes one more gap than the number of objects placed in a row!
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Math Problem Analysis
Mathematical Concepts
Algebra
Division
Subtraction
Problem Solving
Formulas
Total width of frames = number of frames × width of each frame
Remaining space = total width of wall - total width of frames
Interval width = remaining space / number of gaps
Theorems
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Suitable Grade Level
Grades 6-8