a music service has two plans. the platinum plan allows for multiple devices, and the gold plan allows for…

a music service has two plans. the platinum plan allows for multiple devices, and the gold plan allows for one device. last year, the platinum plan had 480,000 members, and the gold plan had 600,000 members. this year, membership in the platinum plan decreased by 30%, and membership in the gold plan increased by 18%. part a to the nearest whole percentage, what was the overall percent change in membership? enter the answer in the box. % part b was the overall change a percent decrease or a percent increase? a. percent decrease b. percent increase

a music service has two plans. the platinum plan allows for multiple devices, and the gold plan allows for one device. last year, the platinum plan had 480,000 members, and the gold plan had 600,000 members. this year, membership in the platinum plan decreased by 30%, and membership in the gold plan increased by 18%. part a to the nearest whole percentage, what was the overall percent change in membership? enter the answer in the box. % part b was the overall change a percent decrease or a percent increase? a. percent decrease b. percent increase

Answer

Explanation:

Step1: Calculate new platinum - plan members

The number of platinum - plan members last year was $480000$. It decreased by $30%$. The new number of platinum - plan members is $480000\times(1 - 0.3)=480000\times0.7 = 336000$.

Step2: Calculate new gold - plan members

The number of gold - plan members last year was $600000$. It increased by $18%$. The new number of gold - plan members is $600000\times(1 + 0.18)=600000\times1.18 = 708000$.

Step3: Calculate total members last year and this year

The total number of members last year is $480000 + 600000=1080000$. The total number of members this year is $336000+708000 = 1044000$.

Step4: Calculate the percent change

The formula for percent change is $\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times100%$. So, $\frac{1044000 - 1080000}{1080000}\times100%=\frac{- 36000}{1080000}\times100%\approx - 3%$.

Answer:

Part A: $-3$ Part B: A. percent decrease