Rita places 9 chairs, the distance between adjacent chairs is 4/5m apart. Find the distance between the first and the last chair
Answers
Answer:
To find the distance between the first and last chair, we must first calculate the overall length of all the chairs, from which we must subtract the edges' distances between the first and second chair and the eighth and ninth chairs.
Step-by-step explanation:
Let's start by finding the distance between adjacent chairs. We know that the distance between adjacent chairs is 4/5m, so we can represent it as d = 4/5m.
Next, we need to find the total distance covered by all the chairs. Since there are nine chairs, there are eight gaps between them. Therefore, the total distance covered by all the chairs is:
Total distance = 8d + 9c
where c is the width of a single chair.
Since we don't know the width of a single chair, we can use a variable to represent it, say x. Then we have:
Total distance = 8d + 9x
Substituting d = 4/5m, we get:
Total distance = 8(4/5)m + 9x
Total distance = 6.4m + 9x
Now we need to find the width of a single chair, x. We know that there are nine chairs placed along the total distance covered by all the chairs, so we can represent the width of a single chair as:
x = (Total distance) / 9
x = (6.4m + 9x) / 9
Simplifying this equation, we get:
8x / 9 = 6.4m / 9
x = 0.9m
Therefore, the width of a single chair is 0.9m.
Now we can find the total distance covered by all the chairs:
Total distance = 8d + 9x
Total distance = 8(4/5)m + 9(0.9)m
Total distance = 6.4m + 8.1m
Total distance = 14.5m
Finally, we need to subtract the distance between the first and second chair and the distance between the eighth and ninth chair:
Distance between first and last chair = Total distance - (distance between first and second chair) - (distance between eighth and ninth chair)
Distance between first and last chair = 14.5m - (4/5)m - (4/5)m
Distance between first and last chair = 13.1m
Therefore, the distance between the first and last chair is 13.1m.
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