Question

When a volcano​ erupts, the height of the peak is reduced and the upper portion is removed. The height of a volcano after it erupted was​ 8,219.5 feet. This was​ 85% of the​ volcano's original height. What was the original​ height?

Answer 1

To find the original height of the volcano, divide the height after the eruption (8,219.5 feet) by 0.85, which represents 85%. The calculation shows that the original height was approximately 9,670 feet.

Step-by-step explanation:

The question asks us to find the original height of a volcano, given that its height after an eruption is 8,219.5 feet, which is 85% of its original height. To calculate the original height, we can set up the following proportion: 85% of the original height is equal to 8,219.5 feet. Converted to a decimal, 85% is 0.85. Thus, we need to divide the post-eruption height by 0.85 to find the original height.

Step-by-step calculation:

1. Convert the percentage to a decimal: 85% = 0.85
2. Divide the post-eruption height by the decimal: Original Height = 8,219.5 feet / 0.85
3. Calculate the result: Original Height = 9,670 feet (rounded to the nearest whole number for simplicity)

Therefore, the original height of the volcano was approximately 9,670 feet.