MATH SOLVE

4 months ago

Q:
# the percent of working students increased 21.7% to 8.9%, what was the percent prior to increase

Accepted Solution

A:

Answer:Approximately 7.3%.Step-by-step explanation:What is percentage increase?[tex]\displaystyle \text{Percentage Increase} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\%[/tex].For this question:[tex]\text{Percentage Increase} = 21.7\%[/tex],[tex]\text{Final Value} = 8.9\% = 0.089[/tex], and[tex]\text{Initial Value}[/tex] needs to be found.Let [tex]\text{Initial Value} = x[/tex].[tex]\displaystyle \frac{0.089 - x}{x} = 0.217[/tex].Assume that [tex]x \ne 0[/tex]. Multiply both sides of the equation by [tex]x[/tex]:[tex]0.089 - x = 0.217x[/tex].Add [tex]x[/tex] to both sides of the equation:[tex]0.089 = (1 + 0.217)x[/tex].[tex]\displaystyle x = \frac{0.089}{1 + 0.217} = 0.0731 \approx 7.3\%[/tex].In other words, the initial percentage is approximately 7.3%.