Question

synthesis
describe a strategy for determining the input when you know the percent change and the output.
use this example if it helps you to explain your thinking.
(image: a factory scene with a sign decrease by 40%, an input box with ?, and an output box with 14.4)

Explanation:

Step1: Understand the percent change

A 40% decrease means the output is (100% - 40%) = 60% of the input. So the output is 0.6 times the input.

Step2: Set up the equation

Let the input be \( x \). Then \( 0.6x = 14.4 \) (using the example).

Step3: Solve for the input

To find \( x \), divide the output by the decimal form of the remaining percentage. So \( x=\frac{14.4}{0.6} \).

Step4: Calculate the value

\( \frac{14.4}{0.6}=24 \). So the strategy is: If there's a percent decrease of \( p\% \), the output is \( (1 - \frac{p}{100}) \) times the input. So to find the input, divide the output by \( (1 - \frac{p}{100}) \). For a percent increase, divide by \( (1+\frac{p}{100}) \).

Answer:

The strategy is to divide the output by \( 1 - \) (percent decrease as a decimal) (or \( 1 + \) percent increase as a decimal) to find the input. For the example, input is 24.