Q4. - Algebra 2

Question

In 2000, Matt had a collection of 30 music CDs. Since then he has given away 2 CDs, purchased 6 new CDs, and traded 3 of his CDs to Kashan for 4 of Kashan’s CDs. Since 2000, what has been the percentage of increase in the number of CDs in Matt’s collection?

$\text{A}. \text{ 3}\frac{1}{3}\% \text{ B. }10\% \text{ C. 14}\frac{2}{7}\% \text{ D. 16}\frac{2}{3}\%$

Step-by-Step Solution

Answer

The percentage of increase in the number of CDs in Matt’s collection is $16\frac{2}{3}\%$.

Step-1 – Apply the concept of increase percentage

Increase percentage is given by

 $\text{increase percentage= }\frac{\text{increase}}{\text{original number}}\times 100$

where increase = new number – original number  

Step-2 – Find the value of New number

Initially Matt had 30 CDs.

Since he gave away 2 CDs, the number of CDs left now is 30-2=28

After this he purchased 6 new CDs. Therefore, the number of CDs he has now is 28+6=34

He then traded 3 of his CDs to Kashan for 4 of Kashan’s CDs. Hence the number of CDs he has is 34-3+4=35

Therefore, the total number of CDs Matt have since 2000 is 35. 

Step-3 – Find the increase percentage

Using original number as 30 and new number as 35 in increase percentage formula, the following is obtained:

$\begin{array}{c}increase\%=\frac{35-30}{30}\times 100\\ =\frac{5}{30}\times 100\\ =\frac{50}{3}\\ =16\frac{2}{3}\end{array}$

Hence the percentage of increase in the number of CDs in Matt’s collection is $16\frac{2}{3}\%$

Therefore, option D is correct.