Question

A stairway consists of 10 stairs, each 7(7)/(8) inches high. What is the vertical height of the stairway?

Answer 1

The vertical height of the stairway is 68(3)/(4) inches.

Step-by-step explanation:

To find the total vertical height of the stairway, you can multiply the number of stairs by the height of each stair. In this case, there are 10 stairs, and each stair is 7(7)/(8) inches high.

The calculation is as follows:

`\[10 \text{ stairs} * 7(7)/(8) \text{ inches/stair} = 68(3)/(4) \text{ inches}.\]`

Therefore, the vertical height of the stairway is 68(3)/(4) inches.

The height of each stair is expressed as a mixed number, and the final answer is also given in the same format for clarity. This format is useful in practical applications, providing a clear and concise representation of the vertical height of the entire stairway. The calculation is straightforward, involving simple multiplication of the number of stairs by the height of each stair, and the use of mixed numbers ensures that the answer is presented in a format that is easy to understand for anyone working with or designing staircases.

Answer 2

The vertical height of the stairway is
`\( (85)/(2) \)` inches.

Step-by-step explanation:

The total vertical height of the stairway can be calculated by multiplying the number of stairs by the height of each stair. In this case, there are 10 stairs, and each stair has a height of
`\( (7)/(8) \)` inches. Therefore, the total vertical height
`(\( H \))` can be found using the formula:

`\[ H = \text{Number of Stairs} * \text{Height of Each Stair} \]`

`\[ H = 10 * (7)/(8) \]`

`\[ H = (70)/(8) \]`

Simplifying the fraction, we get
`\( H = (35)/(4) \)` inches.

Now, to express the answer in a more readable form, we can convert
`\( (35)/(4) \) to \( (85)/(2) \)` inches.

The vertical height of the stairway is
`\( (85)/(2) \)` inches, obtained by multiplying the number of stairs (10) by the height of each stair
`(\( (7)/(8) \) inches)`.

This calculation ensures accuracy in determining the total vertical distance covered by the stairway. The formula used is straightforward, multiplying the number of stairs by the individual stair height. The final result,
`\( (85)/(2) \)` inches, represents the complete vertical extent of the staircase.: