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Difficulty: HardFractions, Decimals, and Percentages

A video streaming service has three subscription tiers: Basic, Standard, and Premium. Originally, 25\frac{2}{5} of the subscribers are on the Basic tier and 45%45\% are on the Standard tier. During a promotional campaign, 14\frac{1}{4} of the Basic subscribers upgrade to the Standard tier, and 20%20\% of the original Standard subscribers upgrade to the Premium tier. If no other subscription changes occur, what percent of the total subscribers are now on the Premium tier?

  1. 24%24\%Answer
  2. B
    26%26\%
  3. C
    35%35\%
  4. D
    65%65\%
  5. E
    9%9\%

Answer

The correct answer is 24%24\% of the total subscribers.
To find the new Premium subscriber percentage, we first convert the basic tier fraction to a percent: 25=40%\frac{2}{5} = 40\%. Since the Standard tier is 45%45\%, the original Premium tier must contain the remaining subscribers, which is 100%−40%−45%=15%100\% - 40\% - 45\% = 15\% of the total. The upgrade represents 20%20\% of the original 45%45\% Standard subscribers, which is 0.20×45%=9%0.20 \times 45\% = 9\% of the total subscribers. Adding this 9%9\% upgrade to the original 15%15\% Premium percentage results in a final percentage of 24%24\%.

Step-by-Step Solution

1
Determine the original subscriber percentages for all three tiers.
Basic: 25=40%\frac{2}{5} = 40\%. Standard: 45%45\%. Premium: 100%−(40%+45%)=15%100\% - (40\% + 45\%) = 15\%.
Establishing the starting percentages allows us to track changes relative to the total subscriber population.
2
Calculate the percentage of total subscribers upgrading from Standard to Premium.
20%20\% of the original 45%45\% Standard subscribers = 0.20×45%=9%0.20 \times 45\% = 9\% of the total subscribers.
Since the upgrade rate is relative to the Standard tier, we multiply the rate by the Standard tier's share of the total population.
3
Calculate the final Premium percentage by adding the upgrade percentage to the original Premium percentage.
15%+9%=24%15\% + 9\% = 24\%.
The final Premium percentage is the sum of the original Premium percentage and the percentage of subscribers who upgraded from Standard.

Key Concept

Calculating percentages of subpopulations and translating them to percentages of the entire population.
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Topics

Fractions, Decimals, and Percentages

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