Chapter 12, Problem 4SAP

To determine

To find: correct option that represents net percentage increase in caps since initial collection.

Answer to Problem 4SAP

B.

Explanation of Solution

Given information:

Let’s use minus sign for removal of caps from the collection and addition sign for addition of caps to the initial collection.

Initial collection of caps $\left(T_c\right)$ = 48

Caps given away $\left(-C_1\right)$ = 13

New caps purchased $\left(C_2\right)$ = 17

Trade of caps $\left(-C_3\right)$ = 6

Addition of different style caps $\left(-C_4\right)$ =8

The options are as follows:

1. 60%
2. $12\frac{1}{2}\%$
3. $16\frac{2}{3}\%$
4. 25%
5. $28\frac{1}{2}\%$

Calculation:

Let the final collection of caps be $T_f$ . The total number of caps since the initial collection can be evaluated as follows:

  $\begin{array}{c}{T}_f=T_c-C_1+C_2-C_3+C_4\\ =48-13+17-6+8\\ =54\end{array}$

The net percentage increase in collection can be evaluated as follows:

  $\begin{array}{c}\text{Net percentage increase in collection}=\frac{T_f-T_c}{T_c}\times 100\%\\ =\frac{54-48}{48}\times 100\%\\ =\frac{6}{48}\times 100\%\\ =\frac{25}{2}\%\\ =12\frac{1}{2}\%\end{array}$

Thus, option B. is correct.