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A group of friends makes a video and posts it on YouTube - Junior Cycle Mathematics - Question 9 - 2018

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A group of friends makes a video and posts it on YouTube. They know that they will be paid approximately €15 for each 10 000 views of the video. Use this information... show full transcript

Worked Solution & Example Answer:A group of friends makes a video and posts it on YouTube - Junior Cycle Mathematics - Question 9 - 2018

Step 1

Work out how many views of the video they would need in order to be paid €45.

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Answer

To find out how many views are needed to earn €45, we start by using the given payment rate of €15 per 10,000 views. The steps are as follows:

  1. Set up the proportion:

    ext{Let } v ext{ = number of views needed.} \\ rac{€15}{10,000 ext{ views}} = rac{€45}{v}
  2. Cross-multiply to solve for v:

    15v=45imes10,00015v=450,00015v = 45 imes 10,000 \\ 15v = 450,000
  3. Divide both sides by 15:

    v = rac{450,000}{15} = 30,000 ext{ views}

Thus, they would need 30,000 views.

Step 2

Work out how much (in euro) they will be paid for 80 000 views of the video.

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Answer

With 80,000 views, the payment can be calculated using the same rate:

  1. Determine how many units of 10,000 views are in 80,000 views:

    rac{80,000}{10,000} = 8 ext{ units}
  2. Calculate the payment:

    8imes15=1208 imes €15 = €120

Therefore, they will be paid €120 for 80,000 views.

Step 3

Work out how much (in euro) they will be paid, on average, for 1 view of the video.

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Answer

To find the average payment per view, we take the total payment for 10,000 views and divide it by 10,000:

  1. Calculate average payment: rac{€15}{10,000} = €0.0015 ext{ per view}

Thus, they will be paid on average €0.0015 for 1 view.

Step 4

Write an expression in x for the profit (in euro) they will get for x views of the video.

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Answer

The profit can be calculated using the revenue generated from views minus the cost of making the video. The formula is:

  1. Profit: extProfit=extRevenueextCost=0.0015x70ext(wherexisthetotalnumberofviews) ext{Profit} = ext{Revenue} - ext{Cost} \\ = 0.0015x - 70 ext{ (where x is the total number of views)}

Step 5

Write an equation in x to represent this information, where x is the total number of views of the video.

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Answer

Given that each of the 7 friends receives €200, we can write:

  1. Set up the equation: rac{0.0015x - 70}{7} = 200

Step 6

Work out the value of x, the total number of views of the video.

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Answer

To find x, we can solve the previous equation:

  1. Multiply both sides by 7:

    0.0015x70=14000.0015x - 70 = 1400
  2. Add 70 to both sides:

    0.0015x=14700.0015x = 1470
  3. Divide by 0.0015:

    x = rac{1470}{0.0015} = 980,000 ext{ views}

Thus, the total number of views of the video is 980,000.

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