Directions: Read the following information carefully and answer the question that follows.

A survey was conducted among a group of 150 college students regarding their usage of three streaming services: Netflix, Hulu, and Prime Video. The ratio of students who use only Netflix to those who use only Hulu is 5:4. The number of students who use only Prime Video is equal to the number of students who use both Netflix and Hulu only. A total of 21 students use all three streaming services. The number of students who use both Netflix and Prime Video only is 40% more than the number of students who use both Hulu and Prime Video only. The number of students who use both Hulu and Prime Video only is 30, which is double the number of students who use only Netflix.

The total number of students who use both Hulu and Prime Video is what percentage of the number of students who use all three streaming services together?

Correct Answer: 242.86%

Step-by-step Explanation:

Let us analyze the given information step-by-step for the three streaming services: Netflix, Hulu, and Prime Video.

1. Number of students using both Hulu and Prime Video only:
It is given that the number of students who use both Hulu and Prime Video only is 30.

$\text{Students using Hulu and Prime Video only}=30$

2. Number of students using only Netflix:
The problem states that 30 is double the number of students who use only Netflix. Therefore:

$\text{Students using only Netflix}=\frac{30}{2}=15$

3. Number of students using only Hulu:
The ratio of students who use only Netflix to those who use only Hulu is 5:4. Let H_only represent the number of students using only Hulu:

$\frac{15}{H_{\text{only}}}=\frac{5}{4}$

Solving for H_only:

$H_{\text{only}}=\frac{15\times 4}{5}=12$

4. Number of students using both Netflix and Prime Video only:
This quantity is 40% more than the number of students who use both Hulu and Prime Video only (30):

$\text{Students using Netflix and Prime Video only}=30+(0.40\times 30)=30+12=42$

5. Number of students using all three services:
It is given that 21 students use all three services (Netflix, Hulu, and Prime Video).

$\text{Students using all three services}=21$

6. Total number of students using both Hulu and Prime Video:
The total number of students using both Hulu and Prime Video is the sum of students using Hulu and Prime Video only and students using all three services:

$\text{Total students using both Hulu and Prime Video}=30+21=51$

7. Percentage Calculation:
We need to find what percentage the total number of students using both Hulu and Prime Video (51) is of the number of students using all three services (21):

$\text{Percentage}=\left(\frac{51}{21}\right)\times 100$

Simplifying the calculation:

$\text{Percentage}=\frac{1700}{7}\%\approx 242.857\%\approx 242.86\%$

Thus, the total number of students who use both Hulu and Prime Video is 242.86% of the number of students who use all three streaming services together.