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Because of a problem in the program, the timer in a video player did not begin counting until the video had been playing for several seconds. The player began counting at 0 seconds, even though the video had already played 190 frames. The video plays 25 frames per second.
How many frames had the video already played when the time was equal to 
-3(2)/(5) seconds?

◻ frames

Because of a problem in the program, the timer in a video player did not begin counting until the video had been playing for several seconds. The player began counting at 00 seconds, even though the video had already played 190190 frames. The video plays 2525 frames per second.\newlineHow many frames had the video already played when the time was equal to 325 -3 \frac{2}{5} seconds?\newline \square frames

Full solution

Q. Because of a problem in the program, the timer in a video player did not begin counting until the video had been playing for several seconds. The player began counting at 00 seconds, even though the video had already played 190190 frames. The video plays 2525 frames per second.\newlineHow many frames had the video already played when the time was equal to 325 -3 \frac{2}{5} seconds?\newline \square frames
  1. Understand the problem: Understand the problem.\newlineWe need to find out how many frames the video had played before the timer started, given that the timer started at 00 seconds but the video had already played 190190 frames. Additionally, we need to calculate the number of frames played during the time that is not counted by the timer, which is 35-\frac{3}{5} seconds before the timer started.
  2. Convert to frames: Convert the time in seconds to frames.\newlineSince the video plays at a rate of 2525 frames per second, we can calculate the number of frames played during 35-\frac{3}{5} seconds by multiplying the time in seconds by the frame rate.
  3. Calculate frames played: Calculate the number of frames played during 3(2)5-\frac{3(2)}{5} seconds.\newlineFirst, convert the mixed number 3(2)/5-3(2)/5 to an improper fraction: 3(2)/(5)=(3×5+2)5=175-3(2)/(5) = -\frac{(3\times5 + 2)}{5} = -\frac{17}{5}.\newlineNow, multiply this by the frame rate (2525 frames per second):\newlineNumber of frames = (175)×25\left(-\frac{17}{5}\right) \times 25
  4. Perform multiplication: Perform the multiplication to find the number of frames.\newlineNumber of frames = (175)×25=17×5=85(-\frac{17}{5}) \times 25 = -17 \times 5 = -85 frames.\newlineThis means that 8585 frames were played during the 3(25)-3\left(\frac{2}{5}\right) seconds before the timer started.
  5. Add frames played: Add the number of frames played before the timer started to the frames played during the uncounted time.\newlineWe know that 190190 frames were played before the timer started counting, and we have calculated that an additional 8585 frames were played during the 35-\frac{3}{5} seconds before that.\newlineTotal frames played = 190190 frames + (85(-85 frames)
  6. Calculate total frames: Calculate the total number of frames played.\newlineTotal frames played = 19085=105190 - 85 = 105 frames.\newlineThis is the number of frames that had been played when the time was equal to 32(25)-\frac{3}{2}\left(\frac{2}{5}\right) seconds.

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