Chapter 6.4, Problem 38STP

To determine

To find: Which of the following represents the greatest percent of change.

Answer to Problem 38STP

Greatest percent of change is in Option H.

Explanation of Solution

Given information:

Given four options.

Percent of change $=\frac{A}{O}\times 100$

Where

  $A=$ Amount of change.

  $O=$ Original amount.

From given information

For option F

Original value of boots $=\$90$

Final value of boots $=\$63$

Amount of change $=$ Final value $-$ Original value

  $\begin{array}{l}\Rightarrow A=63-90\\ \Rightarrow A=-27\end{array}$

Percent of change $=\frac{-27}{90}\times 100$

  $\Rightarrow$ Percent of change $=\frac{-2700}{90}$

  $\Rightarrow$ Percent of change $=-30$

Therefore,

Percent of change is $30\%$ and negative sign indicates percent of decrease.

For Option G

Weight of baby at birth $=$ Original value $=7$ pounds

Weight of baby now $=$ Final value $=10$ pounds

Amount of change $=$ Final value $-$ Original value

  $\begin{array}{l}\Rightarrow A=10-7\\ \Rightarrow A=3\end{array}$

Percent of change $=\frac{3}{7}\times 100$

  $\Rightarrow$ Percent of change $=\frac{300}{7}$

  $\Rightarrow$ Percent of change $=42.857$

Therefore,

Percent of change is $42.857\%$ and positive sign indicates percent of increase.

For Option H

Original cost of bracelet $=$ Original value $=\$12$

Selling price of bracelet $=$ Final value $=\$28$

Amount of change $=$ Final value $-$ Original value

  $\begin{array}{l}\Rightarrow A=28-12\\ \Rightarrow A=16\end{array}$

Percent of change $=\frac{16}{12}\times 100$

  $\Rightarrow$ Percent of change $=\frac{1600}{12}$

  $\Rightarrow$ Percent of change $=133.33$

Therefore,

Percent of change is $133.33\%$ and positive sign indicates percent of increase.

For Option J

Original amount $=\$500$

Final amount $=\$600$

Amount of change $=$ Final value $-$ Original value

  $\begin{array}{l}\Rightarrow A=600-500\\ \Rightarrow A=100\end{array}$

Percent of change $=\frac{100}{500}\times 100$

  $\Rightarrow$ Percent of change $=\frac{10000}{500}$

  $\Rightarrow$ Percent of change $=20$

Therefore,

Percent of change is $20\%$ and positive sign indicates percent of increase.

Therefore

On Comparing precent of change from all the given Options

We can say that

Greatest percent of change is in Option H.