Chapter D, Problem 1E

To determine

For the given amount A and B, find:

  $\left(a\right)$ The percent change if A changes to B.

  $\left(b\right)$ The percent change if B changes to A.

Answer to Problem 1E

Solution:$\left(a\right)$ The percent change if A changes to B is $\underset{\_}{100\%}$ .

  $\left(b\right)$ The percent change if B changes to A is $\underset{\_}{-50\%}$ .

Explanation of Solution

Explanation:Given:

  $A=\$\text{5}00,\text{B}=\$\text{1}000$ .

Formula Used: Percentage change: When an amount $A_1$ changes to a new amount $A_2$ , then the percent change is given by:

  $\frac{A_2-A_1}{A_1}\times 100\%$

Calculation:

  $\left(a\right)$ Using the formula for percentage change, we can write the percentage change when A changes to B as shown below.

  $\frac{B-A}{A}\times 100\%$

Now, we plug in the values of A and B in the above formula and simplify it to get the value in percentage form.

  $\begin{array}{l}\frac{B-A}{A}\times 100\%=\frac{1000-500}{500}\times 100\%\\ =\frac{500}{500}\times 100\%\left(\text{Subtract: 1000}-500=500\right)\\ =\frac{50000}{500}\%\left(\text{Multiply: }500\times 100=50000\right)\\ =100\%\end{array}$

Thus, the percent change if A changes to B is $100\%$ .

  $\left(b\right)$ Now similarly when B changes to A, the percent change formula becomes

  $\frac{A-B}{B}\times 100\%$

Now, we plug in the values of A and B in the above formula and simplify it to get the value in percentage form.

  $\begin{array}{l}\frac{A-B}{B}\times 100\%=\frac{500-1000}{1000}\times 100\%\\ =\frac{-500}{1000}\times 100\%\left(\text{Subtract: 500}-1000=-500\right)\\ =\frac{-50000}{1000}\%\left(\text{Multiply: }500\times 100=50000\right)\\ =-50\%\end{array}$

Thus, the percent change if B changes to A is $-50\%$ .

Conclusion: The percent change if A changes to B is $100\%$ , and the percent change if B changes to A is $-50\%$ .