Question

14 Find the percent increase or decrease for each of the following values (indicate whether each is an increase or a decrease). a. 4x to x/ b. 0.25m to 0.5m 5 c. + 2p to d.y to 0.687 8 р 15 Consider the following relationships. TI. 1

Answer 1

The percentage increase or decrease is given by

$\frac{final\: \text{amount}-original\: \text{amount}}{original\: \text{amount}}\times100\%$

Let us find the percentage increase or decrease for the given cases.

a) 4x to x

$\begin{gathered} \frac{x-4x}{4x}\times100\% \\ \frac{-3x}{4x}\times100\% \\ -0.75\times100\% \\ -75\% \end{gathered}$

Therefore, it is a percentage decrease (-75%) since it is negative.

b) 0.25m to 0.5m

$\begin{gathered} \frac{0.5m-0.25m}{0.25m}\times100\% \\ \frac{0.25m}{0.25m}\times100\% \\ 1\times100\% \\ 100\% \end{gathered}$

Therefore, it is a percentage increase (100%) since it is positive.

c) 1/2p to 5/8p

$\begin{gathered} \frac{\frac{5}{8}p-\frac{1}{2}p}{\frac{1}{2}p}\times100\% \\ \frac{\frac{1}{8}p}{\frac{1}{2}p}\times100\% \\ \frac{1}{8}\times\frac{2}{1}\times100\% \\ \frac{2}{8}\times100\% \\ \frac{1}{4}\times100\% \\ 25\% \end{gathered}$

Therefore, it is a percentage increase (25%) since it is positive

d) y to 0.68y

$\begin{gathered} \frac{0.68y-y}{0.68y}\times100\% \\ \frac{-0.32y}{0.68y}\times100\% \\ -0.47\times100\% \\ -47\% \end{gathered}$

Therefore, it is a percentage decrease (-47%) since it is negative.