Question

The percent of working students increased 21.7% to 8.9%, what was the percent prior to increase​

Answer 1

Approximately 7.3%.

Explanation:

What is percentage increase?

`\displaystyle \text{Percentage Increase} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} * 100\%`.

For this question:

• 
  `\text{Percentage Increase} = 21.7\%`,
• 
  `\text{Final Value} = 8.9\% = 0.089`, and
• 
  `\text{Initial Value}` needs to be found.

Let
`\text{Initial Value} = x`.

`\displaystyle (0.089 - x)/(x) = 0.217`.

Assume that
`x \\e 0`. Multiply both sides of the equation by
`x`:

`0.089 - x = 0.217x`.

Add
`x` to both sides of the equation:

`0.089 = (1 + 0.217)x`.

`\displaystyle x = (0.089)/(1 + 0.217) = 0.0731 \approx 7.3\%`.

In other words, the initial percentage is approximately 7.3%.